What is dba. Permissible noise standards in the apartment. Why are high-pitched sounds dangerous?

Often citizens, especially city residents, complain about excessive noise in apartments and on the street. It is especially annoying (the noise) on weekends and at night. And during the day there is little joy from it, especially if there is a small child in the apartment.

Both experts and the Internet are unanimous in their advice - you need to call the local police officer. But before contacting a law enforcement representative, it is necessary to at least roughly understand the noise levels at which such treatment is justified, and which is only an irritating factor, but is not prohibited.

Permissible noise levels in residential premises

It is regulated by legislative acts, according to which the time of day is divided into periods and for each period the permissible noise level is different.

• 22.00 – 08.00 period of silence, during which the specified level should not exceed 35-40 decibels (this is where this indicator is considered).
• From eight in the morning to ten in the evening, according to the law, it refers to daylight hours and the noise can be a little louder - 40-50 dB.

Many people are interested in why there is such a difference in dB. The thing is that the federal authorities gave only approximate values, and each region sets them independently. For example, in some regions, in particular in the capital, there are additional periods of silence during the day. Usually this is from 13.00 to 15.00. Failure to remain silent during this period is a violation.

It is worth saying that the standards mean the level that cannot cause any harm to human hearing. But many do not understand what these indicators mean. Therefore we give comparison table with noise levels and what to compare with.

• 0-5 dB – nothing or almost nothing is heard.
• 10 – this level can be compared to the slight rustling of leaves on a tree.
• 15 – rustling of leaves.
• 20 – barely audible human whisper (at an approximate distance of one meter).
• 25 – level when a person speaks in a whisper at a distance of a couple of meters.
• 30 decibels compared to what? - a loud whisper, the ticking of the clock on the wall. According to SNiP standards, this level is the maximum permissible at night in residential premises.
• 35 – approximately at this level the conversation is conducted, albeit in muted tones.
• 40 decibels is normal speech. SNiP defines this level as acceptable for daytime.
• 45 is also a standard conversation.
• 50 – the sound a typewriter makes (the older generation will understand).
• 55 – what can this level be compared to? Yes, the same as the top line. By the way, according to European standards, this level is the maximum permissible for class A offices.
• 60 is the level determined by law for ordinary offices.
• 65-70 – loud conversations at a distance of one meter.
• 75 – human cry, laughter.
• 80 is a working motorcycle with a muffler, also this is the level of a working vacuum cleaner with an engine power of 2 kW or more.
• 90 - the sound made by a freight car when moving on a piece of iron and can be heard at a distance of seven meters.
• 95 is the sound of a subway car when moving.
• 100 – at this level a brass band plays and a chainsaw works. The sound of the same power is made by thunder. According to European standards, this is the maximum permissible level for the player’s headphones.
• 105 - this level was allowed in passenger airliners until the 80s. last century.
• 110 – noise made by a flying helicopter.
• 120-125 – the sound of a chipper operating at a distance of one meter.
• 130 – this is how many decibels a starting plane produces.
• 135-145 - a jet plane or rocket takes off with such noise.
• 150-160 – a supersonic aircraft crosses the sound barrier.

All of the above are conditionally divided according to the level of impact on human hearing:

• 0-10 – nothing or almost nothing is heard.
• 15-20 – barely audible.
• 25-30 – quiet.
• 35-45 is already quite noisy.
• 50-55 – clearly audible.
• 60-75 – noisy.
• 85-95 – very noisy.
• 100-115 – extremely noisy.
• 120-125 is an almost unbearable noise level for human hearing. Workers working with a jackhammer must wear special headphones, otherwise hearing loss is guaranteed.
• 130 is the so-called pain threshold; a sound higher than this is already fatal for human hearing.
• 135-155 – without protective equipment (headphones, helmets), a person experiences concussion and brain injury.
• 160-200 – guaranteed rupture of the eardrums and, attention, lungs.

Above 200 decibels can not even be considered, as this is a lethal sound level. It is at this level that the so-called noise weapon operates.

What else

But even lower values ​​can lead to irreversible injuries. For example, long-term exposure to a sound of 70-90 decibels on hearing has a detrimental effect on a person, in particular on the central nervous system. For comparison, this is usually a loud TV playing, the level of music in the car for some “lovers”, the sound in the headphones of the player. If you still want to listen to loud music, be prepared for the fact that you will have to deal with your nerves for a long time.

And if the noise exceeds 100 decibels, then hearing loss is almost guaranteed. And as practice shows, music at this level produces more negativity than pleasure.

In Europe, it is prohibited to place a lot of office equipment in one room, especially if the room is not decorated with sound-absorbing materials. Indeed, in a small room, two computers, a fax machine and a printer can raise the noise level to 70 dB.

In general, in the workplace the maximum noise level can be no more than 110 dB. If somewhere it exceeds 135, then any human presence, even short-term, is prohibited in this area.

If the noise level in the workplace exceeds 65-70 dB, it is recommended to wear special soft earplugs. If they are made with high quality, they should reduce external noise by 30 dB.

Isolating headphones, sold in hardware stores, not only provide maximum protection from almost any noise, but will also protect the temporal lobe of the head.

And in conclusion, let’s say one interesting piece of news that might seem funny to some. Statistics have shown that a city dweller living in constant noise, once in a zone of complete silence, where the noise level does not exceed 20 dB, begins to experience discomfort. What can I say, he begins to feel depressed. This is such a paradox.

The physical characteristic of sound volume is the sound pressure level, in decibels (dB). “Noise” is a disorderly mixture of sounds.

The maximum permissible sound levels (LAmax, dBA) are 15 decibels more than “normal”. For example, for living rooms of apartments, the permissible constant sound level during the daytime is 40 decibels, and the temporary maximum is 55.

Inaudible noise - sounds with frequencies less than 16-20 Hz (infrasound) and more than 20 KHz (ultrasound). Low-frequency vibrations of 5-10 hertz can cause resonance, vibration of internal organs and affect brain function. Low-frequency acoustic vibrations increase aching pain in bones and joints in sick people. Infrasound sources: cars, carriages, thunder from lightning, etc. High-frequency vibrations cause tissue heating. The effect depends on the strength of the sound, the location and properties of its sources.

Powerful fans in bakeries, mills and other enterprises where exhaust hoods are used can make a lot of noise, and the wind blows from their side - wave-like increases the propagation range. A possible reason for their noise is improper installation and the design itself, broken bearings, misalignment, or simple wear and tear of the equipment. You may be fined for this.

High-frequency sound and ultrasound with a frequency of 20-50 kilohertz, with modulation of several hertz - are used to scare away birds from airfields, animals (dogs, for example) and insects (mosquitoes, midges).

In workplaces, the maximum permissible equivalent sound levels for intermittent noise are: the maximum sound level should not exceed 110 dBAI, and for impulsive noise - 125 dBAI. It is prohibited to stay even briefly in areas with sound pressure levels above 135 dB in any octave band.

The noise emitted by a computer, printer and fax in a room without sound-absorbing materials can exceed a level of 70 db. Therefore, it is not recommended to place a lot of office equipment in one room. Equipment that is too noisy should be moved outside the premises where the workplaces are located.

You can reduce the noise level if you use noise-absorbing materials as room decoration and curtains made of thick fabric. Anti-noise earplugs will also help.

When constructing buildings and structures in accordance with modern, more stringent sound insulation requirements, technologies and materials must be used that can provide reliable protection from noise.

For fire alarms: the sound pressure level of the useful audio signal provided by the siren must be at least 75 dBA at a distance of 3 m from the siren and no more than 120 dBA at any point in the protected premises (clause 3.14 NPB 104-03).

A high-power siren and a ship's howler - the pressure is more than 120-130 decibels.

Special signals (sirens and “quacks” - Air Horn) installed on service vehicles are regulated by GOST R 50574 - 2002. Sound pressure level of a signaling device when a special sound is emitted. signal, at a distance of 2 meters along the horn axis, must be no lower than:

116 dB(A) - when installing a sound emitter on the roof of a vehicle;

122 dBA - when installing the radiator in the engine compartment of a vehicle.

Fundamental frequency changes should be from 150 to 2000 Hz. Cycle duration is from 0.5 to 6.0 s.

The horn of a civilian vehicle, according to GOST R 41.28-99 and UNECE Rules No. 28, must produce a continuous and monotonous sound with an acoustic pressure level of no more than 118 decibels. This is the maximum permissible value for car alarms.

If a city dweller, accustomed to constant noise, finds himself in complete silence for some time (in a dry cave, for example, where the noise level is less than 20 db), then he may well experience depression instead of rest.

A sound meter device for measuring sound and noise levels.

To measure the noise level, a sound level meter is used, which is produced in different modifications: household (approximate price - 3-4 tr, measurement ranges: 30-130 dB, 31.5 Hz - 8 kHz, filters A and C), industrial ( integrating, etc.) The most common models: SL, octave, svan. Wide-range noise meters are used to measure infrasonic and ultrasonic noise.

Low and high frequency sounds seem quieter than mid frequency sounds of the same intensity. Taking this into account, the uneven sensitivity of the human ear to sounds of different frequencies is modulated using a special electronic frequency filter, obtaining, as a result of normalization of measurements, the so-called equivalent (energy-weighted) sound level with the dimension dBA (dB(A), then yes - with filter "A").

A person can hear sounds with a volume of 10-15 dB and higher. The maximum frequency range for the human ear is from 20 to 20,000 Hz. Sound with a frequency of 2-3 KHz is better heard (common in telephones and on radios in the MW and LW bands). With age, the auditory range of sounds narrows, especially for high-frequency sounds, decreasing to 18 kilohertz or less.

If there are no sound-absorbing materials (carpets, special coverings) on the walls of the premises, the sound will be louder due to multiple reflections (reverberation, that is, echoes from the walls, ceiling and furniture), which will increase the noise level by several decibels.

Noise scale (sound levels, decibels), in the table

Sound volume - noise level.

Noise is defined as a disordered combination of different sounds having tones of varying strength and frequency. Noise levels must be measured in quantities capable of expressing the degree of sound pressure produced. Such units of noise level measurement are associated with the names of two physicists - Alexander Bell and Heinrich Hertz.

Bels, or more often decibels, express the relative loudness of a sound. At its core, a decibel is ten times the logarithm of the ratio of the intensity of existing sound energy to its value. It is not directly a unit of measurement, but rather an expression of a relationship.

The measurable characteristic of sound is the amount of energy contained in it. That is, its intensity as a flow of this energy. That is why the quantitative characteristic is, for example, expressed in watts per square meter (W/m2). However, the obtained values ​​relative to the reference level of 10−12 W/m2 are so small and incomprehensible to most ordinary people that 1 bel was “adopted” to express the resulting ratios. For example, the noise level of a jet airplane is about 13 bels, or in smaller units 130 decibels (dB). For the human ear, the normal range of noise is defined by the boundaries from 20 to 120 decibels. At sounds above this level, a person can suffer serious injuries to the eardrum and contusion. And 160 dB can be lethal.

All people experience noise in their homes. They consist of those directly arising in the room and penetrating from the outside. In order to protect the health and normal condition of citizens, standards for permissible penetrating noise have been adopted. This is 40 dB during the day and 30 at night. Average indicators of noise level units prove that in approximately 80% of cases, even with normal operation of the radio and TV, conversations, noise penetrating from neighboring apartments remains at a level of 40-45 dB, and sounds from the entrance (elevator movement, door slams) reach 60 dB.

In addition to sound intensity, the human ear is sensitive to noise vibrations. Hertz is a unit of frequency, equal to the frequency of the ongoing periodic process, in which one cycle of such a periodic process occurs in 1 second (that is, 1 oscillation). Therefore, for an objective characterization it is necessary to use both of these units of noise level measurement. Hearing aid humans are more sensitive to vibrations created by high frequencies than by low frequencies. But in industrial and living conditions, everyone is under the influence of the entire spectrum. In this regard, when comparing the sound volume level, it is necessary, in addition to the characteristics of the strength and intensity of the sound in decibels, to also indicate the frequency of vibrations per second.

Chapter from the book “Noise” by English engineer Rupert Taylor, R. Taylor “Noise”

Nowadays, everyone has already heard something about “decibels,” but almost no one knows what it is. The decibel seems to be something of an acoustic equivalent of a "candle" - a unit of luminous intensity - and seems to be associated with the ringing of bells (bell means bell, bell in English). However, this is not at all true: the decibel received its name in honor of Alexander Graham Bell, the inventor of the telephone.

The decibel is not only not a unit of measurement of sound, it is not a unit of measurement at all, at least in the same sense as, for example, volts, meters, grams, etc. If you like, you can even measure the length of hair in decibels, which is absolutely impossible do it in volts. Apparently, this all sounds a little strange, so let's try to clarify. Probably no one will be surprised if I say that the distance from London to Inverness is twenty times greater than from my home to London. I can express any distance by comparing it with the distance from my house to London, say to Piccadilly Circus. The distance from London to John-o-Trots is twenty-six times greater than this last distance, and to Australia 500 times. But this does not mean that Australia is 500 units away from anything All numbers given express only ratios of magnitudes.

One of the measurable characteristics of sound is the amount of energy it contains; The sound intensity at any point can be measured as the flow of energy per unit area and expressed, for example, in watts per square meter (W/m2). When trying to record the intensity of ordinary noise in these units, difficulties immediately arise, since the intensity of the quietest sound that can be perceived by a person with the most acute hearing is approximately 0.000 000 000 001 W/m 2 . One of the loudest sounds that we encounter, not without the risk of harmful consequences, is the noise of a jet aircraft flying at a distance of about 50 m. Its intensity is about 10 W/m2. And at a distance of 100 m from the Saturn rocket launch site, the sound intensity noticeably exceeds 1000 W/m2. It is obvious that it is very difficult to handle numbers expressing sound intensities that lie over such a wide range, regardless of whether we represent them in units of energy or even in the form of ratios. There is a simple, although not entirely obvious, way out of this difficulty. The intensity of the weakest audible sound is 0.000 000 000 001 W/m2. Mathematicians will prefer to write this number this way: 10 -12 W/m2. If this notation is unusual for anyone, let us recall that 10 2 is 10 squared, or 100, and 10 3 is 10 cubed, or 1000. Similarly, 10 -2 means 1/10 2, or 1/100, or 0, 01, and 10 -3 is 1/10 3, or 0.001. Multiplying any number by 10 x means x times multiplying it by 10.

Trying to find the most convenient way expressions of sound intensities, let's try to present them in the form of ratios, taking the value 10 -12 W/m2 as the reference intensity. At the same time, we will note how many times the reference intensity needs to be multiplied by 10 in order to obtain the specified sound intensity. For example, the noise of a jet plane is 10,000,000,000,000 (or 10 13) times higher than our standard, that is, this standard must be multiplied 13 times by 10. This method of expression allows us to significantly reduce the values ​​​​of the numbers expressing the gigantic range of sound intensities; if we denote a single increase of 10 times as 1 bel, we get a “unit” to express ratios. Thus, the noise level of a jet aircraft corresponds to 13 bels. Bel turns out to be too large; It is more convenient to use smaller units, tenths of a bel, which are called decibels. Thus, the noise intensity of a jet engine is 130 decibels (130 dB), but to avoid confusion with any other sound intensity standard, it should be noted that 130 dB is defined relative to a reference level of 10 -12 W/m 2.

If the ratio of the intensity of a given sound to a reference intensity is expressed by some less round number, for example 8300, the conversion to decibels will not be so simple. Obviously, the number of multiplications by 10 will be greater than 3 and less than 4, but lengthy calculations are required to accurately determine this number. How to get around this difficulty? It turns out to be quite simple, since all ratios expressed in units of “tenfold increases” have long been calculated - these are logarithms.

Any number can be represented as 10 to some degree: 100 is 10 2 and therefore 2 is the logarithm of 100 to the base 10; 3 is the logarithm of 1000 to base 10 and, less obviously, 3.9191 is the logarithm of 8300. There is no need to keep saying “base 10” because 10 is the most common logarithm base, and unless otherwise specified, that is what is meant base. In formulas, this value is written as log10 or log.

Using the definition of decibel, we can now write the sound intensity level as:

For example, with a sound intensity of 0.26 (2.6 × 10 -1) W/m 2, the intensity level in dB relative to the standard 10 -12 W/m 2 is equal to

But the logarithm of 2.6 is 0.415; hence the final answer looks like this:

10 × 11.415 = 114 dB(accurate to 1 dB)

It should not be forgotten that decibels are not units of measurement in the same sense as, for example, volts or ohms, and that accordingly they must be treated differently. If two rechargeable batteries 6 V (volts) are connected in series, then the potential difference at the ends of the circuit will be 12 V. What happens if you add another noise of 80 dB to a noise of 80 dB? Noise with a total intensity of 160 dB? No, because when a number doubles, its logarithm increases by 0.3 (accurate to two decimal places). Then, when the sound intensity doubles, the intensity level increases by 0.3 bels, that is, by 3 dB. This is true for any intensity level: doubling the sound intensity results in a 3 dB increase in the intensity level. In table Figure 1 shows how the intensity level, expressed in decibels, increases when sounds of different intensities are added together.

Table No. 1

Now, having solved the mystery of the decibel, let's give a few examples.

Noise level in decibels

In table 2 provides a list of typical noises and their intensity levels in decibels.

Table No. 2

How can you determine the intensity of a given sound? This is quite a difficult task; It is much easier to measure pressure fluctuations in sound waves. In table 3 shows the sound pressure values ​​for sounds of various intensities. From this table it can be seen that the range of sound pressures is not as wide as the range of intensities: pressure increases twice as slowly as intensity. When sound pressure doubles, the energy of the sound wave should increase fourfold - then the speed of the particles of the medium will correspondingly increase. Therefore, if we measure the sound pressure as well as the intensity on a logarithmic scale and, in addition, introduce a factor of 2, we obtain the same values ​​for the intensity level. For example, the sound pressure of the weakest audible sound is approximately 0.00002 N (newton)/m 2, and in the cab of a diesel truck it is 2 N/m 2, therefore, the noise intensity level in the cab is

Table No. 3

When expressing the sound pressure level in decibels, it should be remembered that when the pressure doubles, 6 dB is added. If the noise in the cabin of a diesel truck reaches 106 dB, then the sound pressure will double and amount to 4 N/m2, and the intensity will increase fourfold and reach 0.04 W/m2.

We talked a lot about the measure of sound intensity, but did not touch at all on practical methods for measuring this quantity. Measurable characteristics of a sound wave include intensity, pressure, velocity, and particle displacement. All these characteristics are directly related to each other, and if at least one of them can be measured, the rest can be calculated.

It is not difficult to see or feel the vibration of light objects that are in the path of a sound wave. The operating principle of an oscilloscope, the oldest type of sound level meter, is based on this phenomenon. An oscilloscope consists of a diaphragm with a thin thread attached to the center, a mechanical system to amplify the vibrations, and a stylus that records the displacements of the diaphragm on a paper tape. Such notations are reminiscent of the “wavy lines” we talked about in the previous chapter.

This device was extremely insensitive and was only suitable for confirming the acoustic theories of scientists of that time. The inertia of mechanical parts extremely limited the frequency response and accuracy of the device. Replacing the mechanical amplifier with an optical system and using the photographic method of signal recording made it possible to significantly reduce the inertia of the device. In the device improved in this way, the diaphragm thread was wound on a rotating drum, mounted on an axis, to which a mirror was attached, rotating with the drum. A ray of light fell on the mirror; when the mirror was turned in one direction or the other, which occurred as a result of vibrations of the membrane, the beam was deflected, and these deviations could be recorded on photosensitive paper. It was only with the development of electronics that more or less accurate measuring instruments were developed, and to design a modern portable sound level meter we had to wait for the invention of transistors.

Essentially, a modern sound level meter is an electronic analogue of an old mechanical device. The first step in the measurement process is to convert sound pressure into changes in electrical voltage; the microphone produces this conversion. Currently, such devices use microphones of the most various types: condenser, moving coil, crystal, ribbon, heated wire, Rochelle - this is just a small part of all types of microphones. In our book we will not consider the principles of their operation.

All microphones perform the same basic function, and most have a membrane of one kind or another that is driven by changes in pressure in the sound wave. Displacements of the membrane cause corresponding voltage changes at the microphone terminals. The next step in measurement is amplification and then rectification. alternating current and the final operation is to send a signal to a voltmeter calibrated in decibels. In most of these devices, the voltmeter measures not the maximum, but the “rms values” of the signal, that is, the result of a certain type of averaging, which is used more often than the maximum values.

A conventional voltmeter cannot cover a huge range of sound pressures, and therefore in the part of the device where the signal is amplified, there are several circuits that differ in amplification by 10 dB, which can be switched on in series one after the other. However, an improved model of the old oscilloscope is still widely used. In a cathode ray oscilloscope, the problem of inertia inherent in a mechanical oscilloscope is completely eliminated, since the mass of the electron beam is negligible, and it is easily deflected by the electromagnetic field and draws a curve of voltage fluctuations supplied to the device on the screen.

The resulting oscillographic recording is used for mathematical analysis of the sound wave shape. Oscilloscopes are also extremely useful for measuring impulse noise. As we have already said, a conventional sound level meter continuously determines the RMS values ​​of the signal. But, for example, a sound clap or a gun shot does not generate continuous noise, but creates a single, very powerful, sometimes dangerous for hearing, pressure pulse, which is accompanied by gradually damping pressure fluctuations (Fig. 13). The initial pressure surge can damage hearing or break window glass, but since it is single and short-lived, the root mean square value will not be characteristic of it and can only lead to misunderstanding. Although there are special sound level meters for measuring pulsed sounds, most of them will not be able to register the full rms value of the pulse simply because they do not have time to operate. This is where the oscilloscope comes into its own, instantly plotting an accurate pressure rise curve so that the maximum pressure in a pulse can be measured directly on the screen.

Rice. 13. Typical impulse noise

Perhaps one of the most significant issues in acoustics is the dependence of the behavior of sound on its frequency. The lower frequency limit of human perception of sound is about 30 Hz, and the upper limit is no higher than 18 kHz; therefore, the sound level meter would have to register sounds in the same frequency range. But here a serious difficulty arises. As we will see in the next chapter, the sensitivity of the human ear for different frequencies is far from equal; so, for example, for sounds with a frequency of 30 Hz and 1 kHz to sound equally loud, the sound pressure level of the first of them must be 40 dB higher than the second. And therefore, the sound level meter readings by themselves are not worth much.

Electronics specialists have taken up this problem, and modern sound level meters are equipped with correction circuits consisting of separate chains, by connecting which you can reduce the sensitivity of the sound level meter to low-frequency and very high-frequency sounds and thereby bring the frequency characteristics of the device closer to the properties of the human ear. Typically, the sound level meter contains three correction circuits, designated A, B and C; correction A is most useful; correction B is used only occasionally; correction C has little effect on sensitivity in the range 31.5 Hz - 8 kHz. Some types of sound level meters also use a D correction, which allows the device to be read directly in PN dB units used to measure aircraft noise. Accurate calculation of PN dB is quite complex, but for high noise levels the level in PN dB units is equal to the dB level measured by a D-corrected sound level meter plus 7 dB; In most cases, jet aircraft noise expressed in PN dB is approximately equal to the dB level measured by an A-weighted sound level meter plus 13 dB.

Nowadays, almost everywhere, the noise level is taken to be equal to the level measured in dB using an A-weighted sound level meter, and is expressed in units of dBA. Although the human ear perceives sound incomparably more refined than a sound level meter, and therefore sound levels expressed in dBA by no means correspond exactly to physiological response, the simplicity of this unit makes it extremely convenient for practical use.

The major disadvantage of measuring loudness in dBA is that it underestimates our response to low-frequency sounds and completely ignores the ear's increased sensitivity to the loudness of pure tones.

One of the advantages of the dBA scale is, in particular, the fact that here, as we will see in the next chapter, doubling the volume roughly corresponds to an increase in the noise level by 10 dBA. However, even this scale gives no more than a rough indication of the role of the frequency composition of noise, and since this characteristic of noise is often extremely important, the results of measurements carried out using a sound level meter must be supplemented with data obtained using other instruments.

Frequencies, like intensities, are measured on a logarithmic scale, and the doubling of the number of oscillations per second is taken as the basis. Since, however, the range of frequencies is less wide than the range of intensities, the number of tenfold increases is not calculated, decimal logarithms are not used, and sound frequencies are always expressed by the number of oscillations, or cycles per second. The unit of frequency is one oscillation per second, or 1 hertz (Hz). Determining the sound intensity for each frequency would require an infinite number of measurements. Therefore, as in musical practice, the entire range is divided into octaves. The highest frequency in each octave is twice the lowest. The first, simplest stage of frequency analysis of sound is measuring the sound pressure level within each of 8 or 11 octaves, depending on the frequency range of interest to us; When measuring, the signal from the output of the sound level meter is fed to a set of octave filters, or to an octave bandpass analyzer. The word “band” indicates a particular portion of the frequency spectrum. The analyzer contains 8 or 11 electronic filters. These devices pass only those frequency components of the signal that lie within their band. By turning on the filters one at a time, you can sequentially measure the sound pressure level in each band directly using a sound level meter. But in many cases, even octave analyzers do not provide sufficient information about the signal, and then they resort to more detailed analysis, using half or one-third octave filters. To obtain even more detailed analysis, narrow-band analyzers are used, which “cut” the noise into bands of constant relative width, for example 6% of the average frequency of the band, or into bands with a width of a certain number of hertz, for example 10 or 6 Hz. If the noise spectrum contains pure tones, which often happens, their frequency and amplitude can be accurately determined using a discrete frequency analyzer.

Typically, sound analyzing equipment is very bulky, and therefore its use is limited to laboratories. Quite often, the sound to be examined is recorded via a microphone and amplification circuits of the sound level meter on a high-quality portable tape recorder, using control signals for calibration; then the recording is played back in the laboratory, sending a signal to an analyzer, which automatically draws a frequency spectrum on a paper tape. In Fig. Figure 14 shows spectra of typical noise obtained using octave, one-third octave and narrowband (6 Hz band) analyzers.

Rice. 14. Sound analysis using octave, one-third octave and 6 Hz filters.

However, to measure noise, it is not enough to know the volume level and frequency of the sound. If we talk about environmental noise, it consists of many individual noises of various origins: these are the noise of street traffic, airplanes, industrial noise, as well as noise arising from other types of human activity. If you try to measure the noise level on the street with a conventional sound level meter, you will find that this is an extremely difficult task: the sound level meter needle will continuously fluctuate over a very wide range. What should be taken as the noise level? Maximum countdown? No, this figure is too high and insignificant. Average level? This would be possible, but it is extremely difficult to estimate the average value for any specific period of time, and in order to keep the needle within the scale, you will have to continuously change the gain levels of the sound level meter.

Table No. 4

There are two generally accepted methods for taking into account noise level fluctuations that allow this level to be expressed numerically. The first method uses a so-called statistical distribution analyzer. This device records the relative proportion of time during which the measured noise level is within each of the scale steps, located, for example, every 5 dB. The results of these measurements indicate the fraction of the total time during which each sound level was exceeded. By plotting the numbers presented in table. 4, by connecting the points with a smooth line and establishing the levels that were exceeded 1, 10, 50, 90 and 99% of the time, we can give a satisfactory description of the “noise climate”. These levels are designated as follows: L1, L10, L50, L90 and L99. L1 gives an idea of ​​the maximum value of the noise level, L10 is a characteristic high level, while L90 seems to show the background noise, that is, the level to which the noise decreases when a temporary lull occurs. Of great interest is the difference between the values ​​of L10 and L90; it indicates the extent to which the noise level varies in any given place, and the greater the fluctuations in noise, the greater its irritating effect. However, the L10 level itself is a good indicator of the disturbing effect of traffic noise; this indicator is widely used in measuring and forecasting traffic noise, and taking it into account, the amount of state compensation for victims of noise from new highways and roads is determined (see Chapter 11). So, L10 is the sound level, expressed in dBA, which is exceeded for exactly ten percent of the total measurement time.

Typically, traffic noise fluctuates in a very specific way, so the L10 level serves as an independent, fairly satisfactory indicator of noise, although it only partially represents the statistical picture of noise. If the noise changes randomly, as, for example, occurs when railroad, industrial, and sometimes airplane noise overlaps, the distribution of noise levels varies greatly from point to point. In such cases, it is also advisable to express all statistics in one number. Attempts have been made to invent a formula that includes the entire noise picture, including the scope of noise fluctuations. Such indicators include the “transport noise index” and “noise pollution level”, but the most common indicator is a special kind of average value, denoted Leq. It characterizes the average value of sound energy (as opposed to the arithmetic averaging of levels expressed in dB); sometimes Leq is called the equivalent level of continuous noise, because numerically this value corresponds to the level of such strictly stable noise at which, over the entire measurement period, the microphone would receive the same total amount of energy that enters it with all the irregularities, bursts and emissions of the measured fluctuating noise. In the simplest case, Leq will be, for example, 90 dBA if the noise level was 90 dBA all the time, or if the noise was 93 dBA for half the measurement time and completely absent the rest of the time. Indeed, since doubling the intensity or energy of noise leads to an increase in its level by 3 dB, then in order to keep the total amount of energy constant when doubling the noise intensity, the duration of its action should be halved. Similarly, we obtain the same value of Leq = 90 dBA at a noise level of 100 dBA, if it operates for one tenth of the same period of time. Measuring electricity consumption using an electric meter is done in a similar way. In practice, periods of constant noise levels and periods of complete absence do not occur often, and therefore it is quite difficult to calculate Leq. This is where distribution tables like table come to the rescue. 4, or specially designed automatic meters. The Leq index has two disadvantages: when averaging, short bursts of high-level noise make a larger contribution than periods of noise low level; In addition, an increase in the number of maxima has little effect on the value of Leq. For example, if averaging the noise from 100 trains per day, the equivalent level is Leq = 65 dBA, then when the number of trains doubles, Leq increases by only 3 dBA. In order for the value of Leq to increase in the same way as doubling the volume (that is, as if increasing the level by 10 dBA) of the noise created by each of the trains, their number would have to be increased 10 times. And yet, despite some inferiority, the Leq scale represents the best universal measure of noise currently available. In England it will gradually become as widespread as it is on the continent. It is now being used in England to measure noise exposure to industrial employees.

Another measure is also used, which is essentially much more similar to Leq than it might seem at first glance: this is the standard noise index, unfortunately all too familiar to those who live near large airports. The scale of normalized noise indices is used to characterize the average maximum noise levels of aircraft, expressed in PN dB (the so-called “perceived sound level”, see Acoustic Dictionary), and since it starts from a level of 80 PN dB (about 67 dBA), the value 80 is subtracted from the average maximum level. Theoretically, if only one aircraft produces noise during the measurement, the value of this index will be exactly equal to the average maximum level in PN dB minus 80. With each doubling of the number of aircraft, 4.5 units should be added to this number, and not 3, as for the Leq scale. Although the formula for this index looks somewhat overwhelming, above we were able to actually fully characterize it. If individual aircraft noise peak levels differ by only a few dB, the average value can be calculated arithmetically. Otherwise, noise level values ​​expressed in dB will have to be converted back to intensity values, which requires a table of logarithms and a clear head!

There are many other measures, scales and indices for measuring noise, including phons, sones, nois, various derivatives of PN dB and a number of other criteria, not counting all the international versions of the noise standard indices scale. There is no need to describe other units and indicators. It should be noted that in the USA, the Leq indicator is used to measure noise in the workplace, but when the time of exposure to noise doubles, they add not 3 dB to its value, as in Europe, but 5 dB. Otherwise, dBA, L10 and Leq are applied equally throughout the world.

WHAT ARE DECIBELS?

Universal logarithmic units decibels are widely used in quantitative assessments of the parameters of various audio and video devices in our country and abroad. In radio electronics, in particular in wired communications, technology for recording and reproducing information, decibels are a universal measure.

Decibel - no physical quantity, and the mathematical concept

In electroacoustics, the decibel serves essentially as the only unit for characterizing various levels - sound intensity, sound pressure, loudness, as well as for assessing the effectiveness of noise control measures.

The decibel is a specific unit of measurement, not similar to any of those encountered in everyday practice. The decibel is not an official unit in the SI system of units, although, according to the decision of the General Conference on Weights and Measures, it can be used without restrictions in conjunction with the SI, and the International Chamber of Weights and Measures has recommended its inclusion in this system.

A decibel is not a physical quantity, but a mathematical concept.

In this respect, decibels have some similarities to percentages. Like percentages, decibels are dimensionless and serve to compare two quantities of the same name, which are, in principle, very different, regardless of their nature. It should be noted that the term “decibel” is always associated only with energy quantities, most often with power and, with some reservations, with voltage and current.

A decibel (Russian designation - dB, international - dB) is a tenth of a larger unit - bela 1.

Bel is the decimal logarithm of the ratio of the two powers. If two powers are known R 1 And R 2 , then their ratio, expressed in bels, is determined by the formula:

The physical nature of the powers being compared can be anything - electrical, electromagnetic, acoustic, mechanical - it is only important that both quantities are expressed in the same units - watts, milliwatts, etc.

Let us briefly recall what a logarithm is. Any positive 2 number, both integer and fractional, can be represented by another number to a certain degree.

So, for example, if 10 2 = 100, then 10 is called the base of the logarithm, and the number 2 is the logarithm of the number 100 and is denoted log 10 100 = 2 or log 100 = 2 (read as follows: “the logarithm of one hundred to the base ten is equal to two”).

Logarithms with base 10 are called decimal logarithms and are the most commonly used. For numbers that are multiples of 10, this logarithm is numerically equal to the number of zeros behind the unit, and for other numbers it is calculated on a calculator or found from logarithm tables.

Logarithms with base e = 2.718... are called natural. IN computer technology Logarithms with base 2 are usually used.

Basic properties of logarithms:

Of course, these properties are also true for decimal and natural logarithms. The logarithmic method of representing numbers often turns out to be very convenient, since it allows you to replace multiplication with addition, division with subtraction, exponentiation with multiplication, and root extraction with division.

In practice, bel turned out to be too large a value, for example, any power ratio in the range from 100 to 1000 fits within one bel - from 2 B to 3 B. Therefore, for greater clarity, we decided to multiply the number showing the number of bel by 10 and calculate the resulting product indicator in decibels, i.e., for example, 2 B = 20 dB, 4.62 B = 46.2 dB, etc.

Typically, the power ratio is expressed directly in decibels using the formula:

Operations with decibels are no different from operations with logarithms.

2 dB = 1 dB + 1 dB → 1.259 * 1.259 = 1.585;
3 dB → 1.259 3 = 1.995;
4 dB → 2.512;
5 dB → 3.161;
6 dB → 3.981;
7 dB → 5.012;
8 dB → 6.310;
9 dB → 7.943;
10 dB → 10.00.

The → sign means “matches.”

In a similar way, you can create a table for negative decibel values. Minus 1 dB characterizes a decrease in power by 1/0.794 = 1.259 times, i.e., also by about 26%.

Remember that:

⇒ If R 2 =P 1 i.e. P 2 /P 1 =1 , That N dB = 0 , because log 1=0 .

⇒ If P 2 >P l , then the number of decibels is positive.

⇒ If R 2 < P 1 , then decibels are expressed as negative numbers.

Positive decibels are often called gain decibels. Negative decibels, as a rule, characterize energy losses (in filters, dividers, long lines) and are called attenuation or loss decibels.

There is a simple relationship between the decibels of amplification and attenuation: the same number of decibels with different signs corresponds to reciprocal numbers relationships. If, for example, the relation R 2 /R 1 = 2 → 3 dB , That –3 dB → 1/2 , i.e. 1/R 2 /R 1 = P 1 /R 2

⇒ If R 2 /R 1 represents a power of ten, i.e. R 2 /R 1 = 10 k , Where k - any integer (positive or negative), then NdB = 10k , because lg 10 k = k .

⇒ If R 2 or R 1 equals zero, then the expression for NdB loses its meaning.

And one more feature: the curve that determines the decibel values ​​depending on the power ratios initially grows quickly, then its growth slows down.

Knowing the number of decibels corresponding to one power ratio, you can recalculate for another - a close or multiple ratio. In particular, for power ratios that differ by a factor of 10, the number of decibels differs by 10 dB. This decibel feature should be well understood and firmly remembered - it is one of the foundations of the entire system

The advantages of the decibel system include:

⇒ universality, i.e. the ability to be used when assessing various parameters and phenomena;

⇒ huge differences in converted numbers - from units to millions - are displayed in decibels in numbers of the first hundred;

⇒ natural numbers representing powers of ten are expressed in decibels as multiples of ten;

⇒ reciprocal numbers are expressed in decibels as equal numbers, but with different signs;

⇒ both abstract and named numbers can be expressed in decibels.

The disadvantages of the decibel system include:

⇒ poor clarity: converting decibels into ratios of two numbers or performing the reverse operations requires calculations;

⇒ power ratios and voltage (or current) ratios are converted into decibels using different formulas, which sometimes leads to errors and confusion;

⇒ decibels can only be counted relative to a non-zero level; absolute zero, for example 0 W, 0 V, is not expressed in decibels.

Knowing the number of decibels corresponding to one power ratio, you can recalculate for another - a close or multiple ratio. In particular, for power ratios that differ by a factor of 10, the number of decibels differs by 10 dB. This feature of decibels should be well understood and firmly remembered - it is one of the foundations of the entire system.

Comparing two signals by comparing their powers is not always convenient, since direct measurement of electrical power in the audio and radio frequency range requires expensive and complex instruments. In practice, when working with equipment, it is much easier to measure not the power released by the load, but the voltage drop across it, and in some cases, the current flowing.

Knowing the voltage or current and load resistance, it is easy to determine the power. If measurements are carried out on the same resistor, then:

These formulas are very often used in practice, but note that if voltages or currents are measured at different loads, these formulas do not work and other, more complex relationships should be used.

Using the technique that was used to compile the decibel power table, you can similarly determine what 1 dB of voltage-to-current ratio is equal to. A positive decibel will be equal to 1.122, and a negative decibel will be equal to 0.8913, i.e. 1 dB of voltage or current characterizes an increase or decrease of this parameter by approximately 12% relative to the original value.

The formulas were derived under the assumption that the load resistances are active in nature and there is no phase shift between voltages or currents. Strictly speaking, one should consider the general case and take into account for voltages (currents) the presence of a phase shift angle, and for loads not only active, but total resistance, including reactive components, but this is significant only at high frequencies.

It is useful to remember some commonly encountered decibel values ​​in practice and the power and voltage (current) ratios that characterize them, given in Table. 1.

Table 1. Common decibel values ​​for power and voltage

Using this table and the properties of logarithms, it is easy to calculate what arbitrary logarithm values ​​correspond to. For example, 36 dB of power can be represented as 30+3+3, which corresponds to 1000*2*2 = 4000. We get the same result by representing 36 as 10+10+10+3+3 → 10*10*10* 2*2 = 4000.

COMPARISON OF DECIBELS WITH PERCENTAGES

It was previously noted that the concept of decibels has some similarities with percentages. Indeed, since a percentage expresses the ratio of one number to another, conventionally accepted as one hundred percent, the ratio of these numbers can also be represented in decibels, provided that both numbers characterize power, voltage or current. For power ratio:

For voltage or current ratio:

You can also derive formulas for converting decibels into percentage ratios:

In table 2 provides a translation of some of the most common decibel values ​​into percentage ratios. Various intermediate values ​​can be found from the nomogram in Fig. 1.

Rice. 1. Converting decibels into percentage ratios according to the nomogram

Table 2. Converting decibels to percentage ratios

Let's look at two practical examples to explain the conversion of percentages to decibels.

Example 1. To what level of harmonics in decibels relative to the fundamental frequency signal level does the coefficient correspond? nonlinear distortion at 3%?

Let's use fig. 1. Through the point of intersection of the vertical line 3% with the “voltage” graph, draw a horizontal line until it intersects with the vertical axis and get the answer: –31 dB.

Example 2. What percentage of voltage attenuation corresponds to a change of –6 dB?

Answer. At 50% of the original value.

In practical calculations, the fractional part of the numerical value of decibels is often rounded to a whole number, but this introduces an additional error into the calculation results.

DECIBELS IN RADIO ELECTRONICS

Let's look at a few examples that explain the method of using decibels in radio electronics.

Cable attenuation

Energy losses in lines and cables per unit length are characterized by the attenuation coefficient α, which, with equal input and output resistances of the line, is determined in decibels:

Where U 1 - voltage in an arbitrary section of the line; U 2 - voltage in another section, spaced from the first by a unit length: 1 m, 1 km, etc. For example, a high-frequency cable of type RK-75-4-14 has an attenuation coefficient α at a frequency of 100 MHz = –0.13 dB /m, a twisted pair cable of category 5 at the same frequency has an attenuation of about -0.2 dB/m, and a cable of category 6 is slightly less. Signal attenuation graph unshielded cable twisted pair is shown in Fig. 2.

Rice. 2. Graph of signal attenuation in an unshielded twisted pair cable

Fiber optic cables have significantly lower attenuation values ​​ranging from 0.2 to 3 dB over a cable length of 1000 m. All optical fibers have a complex attenuation versus wavelength relationship that has three "transparency windows" of 850 nm, 1300 nm and 1550 nm . “Transparency window” means the least loss at the maximum signal transmission distance. The signal attenuation graph in fiber optic cables is shown in Fig. 3.

Rice. 3. Graph of signal attenuation in fiber optic cables

Example 3. Find what the voltage will be at the output of a piece of cable RK-75-4-14 long l = 50 m, if a voltage of 8 V with a frequency of 100 MHz is applied to its input. The load resistance and characteristic impedance of the cable are equal, or, as they say, matched.

Obviously, the attenuation introduced by a cable segment is K = –0.13 dB/m * 50 m = –6.5 dB. This decibel value roughly corresponds to a voltage ratio of 0.47. This means that the voltage at the output end of the cable is U 2 = 8 V * 0.47 = 3.76 V.

This example illustrates a very important point: losses in a line or cable increase extremely quickly as their length increases. For a cable section 1 km long, the attenuation will be –130 dB, i.e. the signal will be weakened by more than three hundred thousand times!

Attenuation largely depends on the frequency of the signals - in the audio frequency range it will be much less than in the video range, but the logarithmic law of attenuation will be the same, and with a long line length the attenuation will be significant.

Audio amplifiers

Negative feedback is usually introduced into audio amplifiers in order to improve their quality performance. If the voltage gain of the device is without feedback equals TO , and with feedback TO OS that number showing how many times the gain changes under the influence of feedback is called depth of feedback . It is usually expressed in decibels. In a working amplifier, the coefficients TO And TO OS determined experimentally, unless the amplifier is driven with the feedback loop open. When designing an amplifier, first calculate TO , and then determine the value TO OS in the following way:

where β is the transmission coefficient of the feedback circuit, i.e. the ratio of the voltage at the output of the feedback circuit to the voltage at its input.

The feedback depth in decibels can be calculated using the formula:

Stereo devices must meet additional requirements compared to mono devices. The surround sound effect is achieved only with good channel separation, i.e., when there is no penetration of signals from one channel to another. In practical conditions, this requirement cannot be fully satisfied, and mutual leakage of signals occurs mainly through nodes common to both channels. The quality of channel separation is characterized by the so-called transient attenuation a PZ A measure of crosstalk attenuation in decibels is the ratio of the output powers of both channels when the input signal is applied to only one channel:

Where R D - maximum output power of the current channel; R NE - output power of the free channel.

Good channel separation corresponds to a transition attenuation of 60-70 dB, excellent -90-100 dB.

Noise and background

At the output of any receiving and amplifying device, even in the absence of a useful input signal, an alternating voltage can be detected, which is caused by the device’s own noise. The reasons that cause intrinsic noise can be either external - due to interference, poor filtering of the supply voltage, or internal, due to the intrinsic noise of radio components. The most severe effect is noise and interference arising in the input circuits and in the first amplifier stage, since they are amplified by all subsequent stages. Intrinsic noise degrades the actual sensitivity of the receiver or amplifier.

Noise can be quantified in several ways.

The simplest one is that all noise, regardless of the cause and place of its origin, is converted to the input, i.e., the noise voltage at the output (in the absence of an input signal) is divided by the gain:

This voltage, expressed in microvolts, serves as a measure of its own noise. However, to evaluate a device from the point of view of interference, it is not the absolute value of noise that is important, but the ratio between the useful signal and this noise (signal-to-noise ratio), since the useful signal must be reliably distinguished from the background interference. The signal-to-noise ratio is usually expressed in decibels:

Where R With - specified or rated output power of the useful signal along with noise; R w - noise output power when the useful signal source is turned off; U c - signal and noise voltage across the load resistor; U Sh - noise voltage across the same resistor. This is how the so-called “unweighted” signal-to-noise ratio.

Frequently, audio equipment parameters include the signal-to-noise ratio measured with a weighted filter. The filter allows you to take into account the different sensitivity of human hearing to noise at different frequencies. The most commonly used filter is type A, in which case the designation usually indicates the unit of measurement “dBA” (“dBA”). Using a filter usually gives better quantitative results than for unweighted noise (usually the signal-to-noise ratio is 6-9 dB higher), therefore (for marketing reasons) equipment manufacturers often indicate the “weighted” value. For more information on weighing filters, see the Sound Level Meters section below.

Obviously, for successful operation of the device, the signal-to-noise ratio must be higher than a certain minimum permissible value, which depends on the purpose and requirements for the device. For Hi-Fi class equipment this parameter must be at least 75 dB, for Hi-End equipment - at least 90 dB.

Sometimes in practice they use the inverse ratio, characterizing the noise level relative to the useful signal. The noise level is expressed in the same number of decibels as the signal-to-noise ratio, but with a negative sign.

In descriptions of receiving and amplifying equipment, the term background level sometimes appears, which characterizes in decibels the ratio of the components of the background voltage to the voltage corresponding to a given rated power. The background components are multiples of the mains frequency (50, 100, 150 and 200 Hz) and are measured from the total noise voltage using bandpass filters.

The signal-to-noise ratio does not, however, allow us to judge what part of the noise is caused directly by the circuit elements, and what part is introduced as a result of design imperfections (interference, background). To assess the noise properties of radio components, the concept is introduced noise factor . Noise figure is measured by power and is also expressed in decibels. This parameter can be characterized as follows. If at the input of a device (receiver, amplifier) ​​a useful signal with a power of R With and noise power R w , then the signal-to-noise ratio at the input will be (R With /R w )in After strengthening the attitude (R With /R w )out will be less, since the amplified intrinsic noise of the amplifier stages will be added to the input noise.

Noise figure is the ratio expressed in decibels:

Where TO R - power gain.

Therefore, noise figure represents the ratio of the noise power at the output to the amplified noise power at the input.

Meaning Rsh.in determined by calculation; Rsh.out is measured and TO R usually. known from calculation or after measurement. An ideal amplifier from a noise point of view should only amplify useful signals and should not introduce additional noise. As follows from the equation, for such an amplifier the noise figure is F Sh = 0 dB .

For transistors and ICs intended to operate in the first stages of amplification devices, the noise figure is regulated and given in reference books.

The self-noise voltage also determines another important parameter of many amplification devices - dynamic range.

Dynamic range and adjustments

Dynamic range is the ratio of the maximum undistorted output power to its minimum value, expressed in decibels, at which the acceptable signal-to-noise ratio is still ensured:

The lower the noise floor and the higher the undistorted output power, the wider the dynamic range.

The dynamic range of sound sources - an orchestra, a voice - is determined in a similar way, only here the minimum sound power is determined by the background noise. In order for a device to transmit both the minimum and maximum amplitudes of the input signal without distortion, its dynamic range must be no less than the dynamic range of the signal. In cases where the dynamic range of the input signal exceeds the dynamic range of the device, it is artificially compressed. This is done, for example, when recording sound.

The effectiveness of the manual volume control is checked at two extreme positions of the control. First, with the regulator in the maximum volume position, a voltage with a frequency of 1 kHz is applied to the input of the audio amplifier of such a magnitude that a voltage corresponding to a certain specified power is established at the output of the amplifier. Then the volume control knob is turned to the minimum volume, and the voltage at the amplifier input is raised until the output voltage again becomes equal to the original. The ratio of the input voltage with the control at minimum volume to the input voltage at maximum volume, expressed in decibels, is an indicator of the operation of the volume control.

The examples given do not exhaust the practical cases of applying decibels to assessing the parameters of radio-electronic devices. Knowing general rules, application of these units, it is possible to understand how they are used in other conditions not considered here. When encountering an unfamiliar term defined in decibels, you should clearly imagine the ratio of which two quantities it corresponds to. In some cases this is clear from the definition itself, in other cases the relationship between the components is more complex, and when there is no clear clarity, you should refer to the description of the measurement technique in order to avoid serious errors.

When dealing with decibels, you should always pay attention to the ratio of which units - power or voltage - each specific case corresponds to, i.e. which coefficient - 10 or 20 - should appear before the logarithm sign.

LOGARITHMIC SCALE

The logarithmic system, including decibels, is often used when constructing amplitude-frequency characteristics (AFC) - curves depicting the dependence of the transmission coefficient various devices(amplifiers, dividers, filters) on frequency external influence. To construct a frequency response, a number of points are determined by calculation or experiment, characterizing the output voltage or power at a constant input voltage at different frequencies. A smooth curve connecting these points characterizes the frequency properties of the device or system.

If numerical values ​​are plotted along the frequency axis on a linear scale, i.e., in proportion to their actual values, then such a frequency response will be inconvenient to use and will not be clear: in the area lower frequencies it is compressed, while the higher ones are stretched.

Frequency characteristics are usually plotted on the so-called logarithmic scale. Along the frequency axis, values ​​that are not proportional to the frequency itself are plotted on a scale convenient for work. f , and the logarithm lgf/f o , Where f O - frequency corresponding to the reference point. Values ​​are written against the marks on the axis. f . To construct logarithmic frequency responses, special logarithmic graph paper is used.

When carrying out theoretical calculations, they usually use not just frequency f , and the size ω = 2πf which is called the circular frequency.

Frequency f O , corresponding to the origin, can be arbitrarily small, but cannot be equal to zero.

On the vertical axis the ratio of the transmission coefficients at various frequencies to its maximum or average value is plotted in decibels or in relative numbers.

The logarithmic scale allows you to display a wide range of frequencies on a small segment of the axis. On such an axis, equal ratios of two frequencies correspond to sections of equal length. The interval characterizing a tenfold increase in frequency is called decade ; corresponds to a double frequency ratio octave (this term is borrowed from music theory).

Frequency range with cutoff frequencies f H And f IN occupies a stripe in decades f B /f H = 10m , Where m - the number of decades, and in octaves 2 n , Where n - number of octaves.

If a band of one octave is too wide, then intervals with a smaller frequency ratio of half an octave or a third of an octave can be used.

The average frequency of an octave (half an octave) is not equal to the arithmetic mean of the lower and upper frequencies of the octave, but is equal to 0.707f IN .

Frequencies found in this way are called root mean square.

For two adjacent octaves, the mid frequencies also form octaves. Using this property, one can optionally consider the same logarithmic series of frequencies either as boundaries of octaves or as their average frequencies.

On forms with a logarithmic grid, the middle frequency divides the octave row in half.

On a frequency axis on a logarithmic scale, for every third of an octave there are equal segments of the axis, each one third of an octave long.

When testing electroacoustic equipment and conducting acoustic measurements, it is recommended to use a number of preferred frequencies. The frequencies of this series are terms of a geometric progression with a denominator of 1.122. For convenience, some frequencies have been rounded to within ±1%.

The interval between recommended frequencies is one sixth of an octave. This was not done by chance: the series contains a sufficiently large set of frequencies for different types measurements and includes series of frequencies at intervals of 1/3, 1/2 and a whole octave.

And one more important property of a number of preferred frequencies. In some cases, not an octave, but a decade is used as the main frequency interval. So, the preferred range of frequencies can equally be considered both binary (octave) and decimal (decadal).

The denominator of the progression, on the basis of which the preferred range of frequencies is built, is numerically equal to 1 dB of voltage, or 1/2 dB of power.

REPRESENTATION OF NAMED NUMBERS IN DECIBELS

Until now, we assumed that both the dividend and the divisor under the logarithm sign have an arbitrary value and to perform decibel conversion it is important to know only their ratio, regardless of the absolute values.

Specific values ​​of powers, as well as voltages and currents can also be expressed in decibels. When the value of one of the terms under the logarithm sign in the previously discussed formulas is given, the second term of the ratio and the number of decibels will uniquely determine each other. Consequently, if you set any reference power (voltage, current) as a conditional comparison level, then another power (voltage, current) compared with it will correspond to a strictly defined number of decibels. In this case, zero decibel corresponds to power equal to the power of the conventional comparison level, since when N P = 0 R 2 =P 1 therefore this level is usually called zero. Obviously, at different zero levels, the same specific power (voltage, current) will be expressed in different numbers of decibels.

Where R - power to be converted into decibels, and R 0 - zero power level. Magnitude R 0 is placed in the denominator, while power is expressed in positive decibels P > P 0 .

The conditional power level with which the comparison is made can, in principle, be any, but not everyone would be convenient for practical use. Most often, the zero level is set to 1 mW of power dissipated in a 600 Ohm resistor. The choice of these parameters occurred historically: initially, the decibel as a unit of measurement appeared in technology telephone communication. The characteristic impedance of overhead two-wire copper lines is close to 600 Ohms, and a power of 1 mW is developed without amplification by a high-quality carbon telephone microphone at a matched load impedance.

For the case when R 0 = 1 mW=10 –3 Tue: P R = 10 log P + 30

The fact that the decibels of the represented parameter are reported relative to a certain level is emphasized by the term “level”: interference level, power level, volume level

Using this formula, it is easy to find that relative to the zero level of 1 mW, the power of 1 W is defined as 30 dB, 1 kW as 60 dB, and 1 MW is 90 dB, i.e., almost all the powers encountered fit into within the first hundred decibels. Powers less than 1 mW will be expressed in negative decibel numbers.

Decibels defined relative to the 1 mW level are called decibel milliwatts and are denoted dBm or dBm. The most common values ​​for zero levels are summarized in Table 3.

In a similar way, we can present formulas for expressing voltages and currents in decibels:

Where U And I - voltage or current to be converted, a U 0 And I 0 - zero levels of these parameters.

The fact that the decibels of the represented parameter are reported relative to a certain level is emphasized by the term “level”: interference level, power level, volume level.

Microphone sensitivity , i.e. the ratio of the electrical output signal to the sound pressure acting on the diaphragm, is often expressed in decibels, comparing the power developed by the microphone at the nominal load impedance with the standard zero power level P 0 =1 mW . This microphone setting is called standard level microphone sensitivity . Typical test conditions are considered to be a sound pressure of 1 Pa with a frequency of 1 kHz, and a load resistance for a dynamic microphone of 250 Ohms.

Table 3. Zero levels for measuring named numbers

The power developed by a dynamic microphone is naturally extremely low, much less than 1 mW, and the sensitivity level of the microphone is therefore expressed in negative decibels. Knowing the standard sensitivity level of the microphone (it is given in the passport data), you can calculate its sensitivity in voltage units.

In recent years, to characterize the electrical parameters of radio equipment, other values ​​have begun to be used as zero levels, in particular 1 pW, 1 μV, 1 μV/m (the latter for estimating field strength).

Sometimes it becomes necessary to recalculate a known power level P R or voltage P U , specified relative to one zero level R 01 (or U 01 ) another R 02 (or U 02 ). This can be done using the following formula:

The ability to represent both abstract and named numbers in decibels leads to the fact that the same device can be characterized by different numbers of decibels. This duality of decibels must be kept in mind. A clear understanding of the nature of the parameter being determined can serve as protection against errors.

To avoid confusion, it is advisable to specify the reference level explicitly, for example –20 dB (relative to 0.775 V).

When converting power levels into voltage levels and vice versa, it is necessary to take into account the resistance, which is standard for this task. Specifically, the dBV for a 75 ohm TV circuit is (dBm–11dB); dBµV for a 75-ohm TV circuit corresponds to (dBm+109dB).

DECIBELS IN ACOUSTICS

Until now, when talking about decibels, we have used electrical terms - power, voltage, current, resistance. Meanwhile, logarithmic units are widely used in acoustics, where they are the most frequently used unit in quantitative assessments of sound quantities.

Sound pressure R represents the excess pressure in a medium relative to the constant pressure existing there before the sound waves appear (unit is pascal (Pa)).

An example of sound pressure (or sound pressure gradient) receivers is most types of modern microphones, which convert this pressure into proportional electrical signals.

Sound intensity is related to sound pressure and the vibrational speed of air particles by a simple relationship:

J=pv

If a sound wave propagates in free space where there is no reflection of sound, then

v=p/(ρc)

here ρ is the density of the medium, kg/m3; With - speed of sound in the medium, m/s. Product ρ c characterizes the environment in which sound energy propagates and is called specific acoustic resistance . For air at normal atmospheric pressure and temperature 20°C ρ c =420 kg/m2*s; for water ρ c = 1.5*106 kg/m2*s.

We can write that:

J=p 2 / (ρс)

everything that has been said about the conversion of electrical quantities into decibels applies equally to acoustic phenomena

If we compare these formulas with the formulas derived earlier for power. current, voltage and resistance, then it is easy to detect an analogy between individual concepts characterizing electrical and acoustic phenomena and equations describing quantitative dependencies between them.

Table 4. Relationship between electrical and acoustic characteristics

The analogue of electrical power is acoustic power and sound intensity; the analogue of voltage is sound pressure; electricity corresponds to the oscillatory speed, and the electrical resistance corresponds to the specific acoustic impedance. By analogy with Ohm's law for electrical circuit we can talk about Ohm's acoustic law. Consequently, everything that has been said about the conversion of electrical quantities into decibels applies equally to acoustic phenomena.

The use of decibels in acoustics is very convenient. The intensities of sounds encountered in modern conditions can vary hundreds of millions of times. Such a huge range of changes in acoustic quantities creates great inconvenience when comparing their absolute values, but when using logarithmic units this problem is eliminated. In addition, it has been established that the loudness of a sound, when assessed by ear, increases approximately in proportion to the logarithm of the sound intensity. Thus, the levels of these quantities, expressed in decibels, correspond fairly closely to the volume perceived by the ear. For most people with normal hearing, a change in the volume of a 1 kHz sound is perceived as a change in sound intensity of approximately 26%, i.e., 1 dB.

In acoustics, by analogy with electrical engineering, the definition of decibels is based on the ratio of two powers:

Where J 2 And J 1 - acoustic powers of two arbitrary sound sources.

Similarly, the ratio of two sound intensities is expressed in decibels:

The last equation is valid only if acoustic resistance, in other words, the constancy of the physical parameters of the medium in which sound waves propagate.

The decibels determined by the above formulas are not related to the absolute values ​​of acoustic quantities and are used to evaluate sound attenuation, for example, the effectiveness of sound insulation and noise suppression and attenuation systems. Unevenness of frequency characteristics is expressed in a similar way, i.e. the difference between the maximum and minimum values ​​in a given frequency range of various sound emitters and receivers: microphones, loudspeakers, etc. In this case, the counting is usually carried out from the average value of the value under consideration, or (when working in sound range) relative to the value at a frequency of 1 kHz.

In the practice of acoustic measurements, however, as a rule, one has to deal with sounds, the values ​​of which must be expressed in specific numbers. The equipment for carrying out acoustic measurements is more complex than the equipment for electrical measurements, and is significantly inferior in accuracy. In order to simplify measurement techniques and reduce errors in acoustics, preference is given to measurements relative to reference, calibrated levels, the values ​​of which are known. For the same purpose, to measure and study acoustic signals, they are converted into electrical signals.

The absolute values ​​of powers, sound intensities and sound pressures can also be expressed in decibels if in the above formulas they are specified by the values ​​of one of the terms under the logarithm sign. By international agreement, the sound intensity reference level (zero level) is considered to be J 0 = 10 –12 W/m 2 . This insignificant intensity, under the influence of which the amplitude of vibrations of the eardrum is less than the size of an atom, is conventionally considered to be the hearing threshold of the ear in the frequency range of the greatest sensitivity of hearing. It is clear that all audible sounds are expressed relative to this level only in positive decibels. The actual hearing threshold for people with normal hearing is slightly higher and is 5-10 dB.

To represent sound intensity in decibels relative to a given level, use the formula:

The intensity value calculated using this formula is usually called sound intensity level .

The sound pressure level can be expressed in a similar way:

In order for the sound intensity and sound pressure levels in decibels to be expressed numerically as one value, the zero sound pressure level (sound pressure threshold) must be taken to be:

Example. Let us determine what intensity level in decibels is created by an orchestra with a sound power of 10 W at a distance r = 15 m.

The sound intensity at a distance r = 15 m from the source will be:

Intensity level in decibels:

The same result will be obtained if you convert not the intensity level into decibels, but the sound pressure level.

Since at the place where sound is received, the sound intensity level and the sound pressure level are expressed by the same number of decibels, in practice the term “decibel level” is often used without indicating which parameter these decibels refer to.

By determining the level of intensity in decibels at any point in space at a distance r 1 from the sound source (calculated or experimentally), it is easy to calculate the intensity level at a distance r 2 :

If the sound receiver is simultaneously affected by two or more sound sources and the sound intensity in decibels created by each of them is known, then to determine the resulting decibel value, the decibels should be converted into absolute intensity values ​​(W/m2), added up, and this sum again converted to decibels. In this case, it is impossible to add the decibels at once, since this would correspond to the product of the absolute values ​​of the intensities.

If available n several identical sound sources with the level of each L J , then their total level will be:

If the intensity level of one sound source exceeds the levels of the others by 8-10 dB or more, only this one source can be taken into account and the effects of the others can be neglected.

In addition to the considered acoustic levels, you can sometimes come across the concept of the sound power level of a sound source, determined by the formula:

Where R - sound power of the characterized arbitrary sound source, W; R 0 - initial (threshold) sound power, the value of which is usually taken equal to P 0 = 10 –12 W.

VOLUME LEVELS

The sensitivity of the ear to sounds of different frequencies varies. This dependence is quite complex. At low sound intensity levels (up to approximately 70 dB), the maximum sensitivity is 2-5 kHz and decreases with increasing and decreasing frequency. Therefore, sounds of the same intensity but different frequencies will sound different in volume. As the sound intensity increases, the frequency response of the ear levels out and at high intensity levels (80 dB and above), the ear reacts approximately equally to sounds of different frequencies in the audio range. It follows from this that sound intensity, which is measured by special broadband devices, and volume, which is recorded by the ear, are not equivalent concepts.

The volume level of a sound of any frequency is characterized by the value of the level of a sound equal in volume with a frequency of 1 kHz

The volume level of a sound of any frequency is characterized by the level of a sound equal in volume with a frequency of 1 kHz. Loudness levels are characterized by so-called equal loudness curves, each of which shows what level of intensity at different frequencies a sound source must develop to give the impression of equal loudness to a 1 kHz tone of a given intensity (Fig. 4).

Rice. 4. Equal Loudness Curves

Equal loudness curves essentially represent a family of ear frequency responses on a decibel scale for different intensity levels. The difference between them and conventional frequency responses lies only in the method of construction: the “blockage” of the characteristic, i.e., a decrease in the transmission coefficient, is represented here by an increase rather than a decrease in the corresponding section of the curve.

The unit characterizing the volume level, in order to avoid confusion with intensity and sound pressure decibels, has been given a special name - background .

The sound volume level in the backgrounds is numerically equal to the sound pressure level in decibels of a pure tone with a frequency of 1 kHz, equal in volume.

In other words, one hum is 1 dB SPL of a 1 kHz tone corrected for ear frequency response. There is no constant relationship between these two units: it changes depending on the volume level of the signal and its frequency. Only for currents with a frequency of 1 kHz, the numerical values ​​for the volume level in the background and the intensity level in decibels are the same.

If we refer to Fig. 4 and trace the course of one of the curves, for example, for a level of 60 von, it is easy to determine that to ensure equal volume with a tone of 1 kHz at a frequency of 63 Hz, a sound intensity of 75 dB is required, and at a frequency of 125 Hz only 65 dB.

High-quality audio amplifiers use manual volume controls with loudness compensation, or, as they are also called, compensated controls. Such regulators, simultaneously with adjusting the input signal value downwards, provide an increase in the frequency response in the lower frequency region, due to which a constant sound timbre is created for the ear when different volumes sound playback.

Research has also established that doubling the sound volume (as assessed by hearing) is approximately equivalent to changing the volume level by 10 backgrounds. This dependence is the basis for estimating sound volume. Per unit of loudness, called dream , the volume level is conventionally assumed to be 40 background. Double volume equal to two sons corresponds to 50 backgrounds, four sons corresponds to 60 backgrounds, etc. The conversion of volume levels into volume units is made easier by the graph in Fig. 5.

Rice. 5. Relationship between loudness and loudness level

Most of the sounds we encounter in everyday life are noise in nature. Characterizing the loudness of noise based on comparison with pure tones of 1 kHz is simple, but leads to the fact that the assessment of noise by ear may diverge from the readings of measuring instruments. This is explained by the fact that at equal levels of noise volume (in the background), the most irritating effect on a person is exerted by noise components in the range of 3-5 kHz. Noises may be perceived as equally unpleasant even though their volume levels are not equal.

The irritating effect of noise is more accurately assessed by another parameter, the so-called perceived noise level . A measure of perceived noise is the sound level of uniform noise in an octave band with an average frequency of 1 kHz, which, under given conditions, is rated by the listener as equally unpleasant as the measured noise. Perceived noise levels are characterized by units of PNdB or PNdB. They are calculated using a special method.

A further development of the noise assessment system is the so-called effective perceived noise levels, expressed in EPNdB. The EPNdB system allows you to comprehensively assess the nature of the noise impact: frequency composition, discrete components in its spectrum, as well as the duration of noise exposure.

By analogy with the loudness unit sleep, a noise unit has been introduced - Noah .

In one Noah The noise level of uniform noise in the band 910-1090 Hz at a sound pressure level of 40 dB is assumed. In other respects, noi are similar to sons: a doubling of noise level corresponds to an increase in the level of perceived noise by 10 PNdB, i.e. 2 noi = 50 PNdB, 4 noi = 60 PNdB, etc.

When working with acoustic concepts, keep in mind that sound intensity represents an objective physical phenomenon that can be accurately defined and measured. It really exists whether anyone hears it or not. The loudness of a sound determines the effect that the sound produces on the listener, and is therefore a purely subjective concept, since it depends on the state of the person’s hearing organs and his personal abilities to perceive sound.

SOUND MEASURES

To measure all kinds of noise characteristics special devices are used - sound level meters. A sound level meter is a self-contained, portable device that allows you to measure sound intensity levels directly in decibels over a wide range relative to standard levels.

A sound level meter (Fig. 6) consists of a high-quality microphone, a wide-range amplifier, a sensitivity switch that changes the gain in 10 dB steps, a frequency response switch and a graphic indicator, which usually provides several options for presenting the measured data - from numbers and tables to graphs.

Rice. 6. Portable digital sound level meter

Modern sound level meters are very compact, which allows measurements to be taken in hard-to-reach places. Among the domestic sound level meters, one can name the device of the Octava-Electrodesign company “Octava-110A” (http://www.octava.info/?q=catalog/soundvibro/slm).

Sound level meters can determine both general sound intensity levels when measuring with a linear frequency response, and background sound levels when measuring with frequency characteristics similar to those of the human ear. The range of measurements of sound pressure levels is usually in the range from 20-30 to 130-140 dB relative to the standard sound pressure level of 2 * 10–5 Pa. Using interchangeable microphones, the measurement level can be expanded up to 180 dB.

Depending on metrological parameters and technical characteristics domestic sound level meters are divided into first and second classes.

The frequency characteristics of the entire sound level meter path, including the microphone, are standardized. There are five frequency responses in total. One of them is linear within the entire operating frequency range ( symbol Lin), the other four approximate the characteristics of the human ear for pure tones at different volume levels. They are named by the first letters of the Latin alphabet A, B, C And D . The appearance of these characteristics is shown in Fig. 7. The frequency response switch is independent of the measurement range switch. For class 1 sound level meters, the required characteristics are: A, B, C And Lin . Frequency response D - additional. Sound level meters of the second class must have the characteristics A And WITH ; the rest are permitted.

Rice. 7. Standard frequency characteristics of sound level meters

Characteristic A imitates an ear at approximately 40 background. This characteristic is used when measuring weak noises - up to 55 dB and when measuring volume levels. In practical conditions, the frequency response with correction is most often used A . This is explained by the fact that, although human perception of sound is much more complex than the simple frequency dependence that determines the characteristic A , in many cases, the measurement results of the device are in good agreement with the assessment of auditory noise at low volume levels. Many standards - domestic and foreign - recommend that noise assessment be carried out according to the characteristics A regardless of the actual sound intensity level.

Characteristic IN repeats the characteristic of the ear at level 70 background. It is used when measuring noise in the range of 55-85 dB.

Characteristic WITH uniform in the range 40-8000 Hz. This characteristic is used when measuring significant volume levels - from 85 von and above, when measuring sound pressure levels - regardless of the measurement limits, as well as when connecting devices to a sound level meter to measure the spectral composition of noise in cases where the sound level meter does not have a frequency response Lin .

Characteristic D - auxiliary. It represents the average response of the ear at approximately 80 von, taking into account the increase in its sensitivity in the band from 1.5 to 8 kHz. When using this characteristic, the sound level meter readings correspond more accurately than other characteristics to the level of perceived noise by a person. This characteristic is used mainly when assessing the irritating effect of high-intensity noise (airplanes, high-speed cars, etc.).

The sound level meter also includes a switch Fast - Slow - Impulse , which controls the timing characteristics of the device. When the switch is set to Fast , the device manages to monitor rapid changes sound levels, in position Slowly the device shows the average value of the measured noise. Time characteristic Pulse used when recording short sound pulses. Some types of sound level meters also contain an integrator with a time constant of 35 ms, simulating the inertia of human sound perception.

When using a sound level meter, the measurement results will vary depending on the set frequency response. Therefore, when recording readings, to avoid confusion, the type of characteristic at which the measurements were made is also indicated: dB ( A ), dB ( IN ), dB ( WITH ) or dB ( D ).

To calibrate the entire microphone-meter path, the sound level meter usually includes an acoustic calibrator, the purpose of which is to create uniform noise at a certain level.

According to the currently valid instruction “Sanitary standards for permissible noise in the premises of residential and public buildings and in residential areas,” the standardized parameters of continuous or intermittent noise are sound pressure levels (in decibels) in octave frequency bands with average frequencies 63, 125, 250, 500, 1000, 2000, 4000, 8000 Hz. For intermittent noise, for example noise from passing vehicles, the normalized parameter is the sound level in dB( A ).

The following total sound levels, measured on the A scale of a sound level meter, have been established: residential premises - 30 dB, classrooms and classrooms of educational institutions - 40 dB, residential areas and recreation areas - 45 dB, work premises of administrative buildings - 50 dB ( A ).

For a sanitary assessment of the noise level, corrections are made to the sound level meter readings from –5 dB to +10 dB, which take into account the nature of the noise, the total time of its action, the time of day and the location of the object. For example, during the daytime, the permissible noise standard in residential premises, taking into account the amendment, is 40 dB.

Depending on the spectral composition of the noise, the approximate norm of maximum permissible levels, dB, is characterized by the following figures:

In the absence of a sound level meter, an approximate estimate of the volume levels of various noises can be made using a table. 5.

Table 5. Noises and their assessment