How is the strength of sound measured? Power standards and other concepts of sound engineering. Mathematical calculation of decibels
Sound are called mechanical vibrations of particles of an elastic medium (air, water, metal, etc.), subjectively perceived by the organ of hearing. Sound sensations are caused by vibrations of the medium occurring in the frequency range from 16 to 20,000 Hz. Sounds with frequencies below this range are called infrasound, and those above are called ultrasound.
Sound pressure- variable pressure in a medium due to the propagation of sound waves in it. The magnitude of sound pressure is estimated by the force of the sound wave per unit area and is expressed in newtons per square meter (1 n/meter square = 10 bar).
Sound pressure level- the ratio of the sound pressure value to the zero level, which is taken as sound pressure n/square meter:
Sound speed depends on the physical properties of the medium in which mechanical vibrations propagate. Thus, the speed of sound in air is 344 m/sec at T=20°С, in water 1,481 m/sec (at T=21.5°С), in wood 3,320 m/sec and in steel 5,000 m/sec sec.
Sound power (or intensity)- the amount of sound energy passing per unit time through a unit area; measured in watts per square meter (W/m2).
It should be noted that sound pressure and sound intensity are related to each other by a quadratic relationship, i.e., with an increase in sound pressure by 2 times, the sound intensity increases 4 times.
Sound level- the ratio of the strength of a given sound to the zero (standard) level, for which the sound strength is taken to be watts/m2, expressed in decibels:
Sound pressure levels and sound intensity, expressed in decibels, are the same in magnitude.
Hearing threshold- the quietest sound that a person can still hear at a frequency of 1000 Hz, which corresponds to sound pressure n/m2.
Sound volume- the intensity of the sound sensation caused by a given sound in a person with normal hearing. The volume depends on the strength of the sound and its frequency, varies proportionally to the logarithm of the sound intensity and is expressed by the number of decibels by which the given sound exceeds in intensity the sound taken as the threshold of audibility. The unit of loudness is background.
Pain threshold- sound pressure or sound intensity, perceived as a painful sensation. The pain threshold depends little on frequency and occurs at a sound pressure of about 50 n/m2.
Dynamic range- the range of sound volumes, or the difference in sound pressure levels of the loudest and quietest sounds, expressed in decibels.
Diffraction- deviation from the rectilinear propagation of sound waves.
Refraction- a change in the direction of propagation of sound waves caused by differences in speed along different sections of the path.
Interference- the addition of waves of the same length arriving at a given point in space along several different paths, as a result of which the amplitude of the resulting wave at different points turns out to be different, and the maxima and minima of this amplitude alternate with each other.
Beats- interference of two sound vibrations that differ little in frequency. The amplitude of the resulting oscillations periodically increases or decreases in time with a frequency equal to the difference between the interfering oscillations.
Reverberation- residual “after-sound” in enclosed spaces. It is formed due to repeated reflection from surfaces and simultaneous absorption of sound waves. Reverberation is characterized by a period of time (in seconds) during which the sound intensity decreases by 60 dB.
Tone- sinusoidal sound vibration. The pitch of the tone is determined by the frequency of sound vibrations and increases with increasing frequency.
Base tone- the lowest tone created by a sound source.
Overtones- all tones, except the main one, created by the sound source. If the frequencies of the overtones are an integer number of times greater than the frequency of the fundamental tone, then they are called harmonic overtones (harmonics).
Timbre- “color” of sound, which is determined by the number, frequency and intensity of overtones.
Combination tones- additional tones arising due to the nonlinearity of the amplitude characteristics of amplifiers and sound sources. Combination tones appear when the system is exposed to two or more vibrations with different frequencies. The frequency of combination tones is equal to the sum and difference of the frequencies of the fundamental tones and their harmonics.
Interval- the ratio of the frequencies of the two sounds being compared. The smallest distinguishable interval between two musical sounds adjacent in frequency (each musical sound has a strictly defined frequency) is called a semitone, and a frequency interval with a 2:1 ratio is called an octave (a musical octave consists of 12 semitones); an interval with a ratio of 10:1 is called a decade.
The unit of the absolute loudness scale is background. A volume of 1 phon is the volume of a continuous pure sine tone with a frequency of 1 kHz, producing a sound pressure of 2 mPa.
Sound volume level- relative value. It is expressed in backgrounds and is numerically equal to the sound pressure level (in decibels - dB) created by a sinusoidal tone with a frequency of 1 kHz of the same volume as the sound being measured (equally loud to the given sound).
Dependence of volume level on sound pressure and frequency
The figure on the right shows a family of equal loudness curves, also called isophones. They are standardized graphs (international standard ISO 226) dependences of the sound pressure level on frequency at a given volume level. Using this diagram, you can determine the volume level of a pure tone of any frequency, knowing the level of sound pressure it creates.
Sound surveillance equipment
For example, if a sine wave with a frequency of 100 Hz creates a sound pressure level of 60 dB, then by drawing straight lines corresponding to these values on the diagram, we find at their intersection an isophone corresponding to a volume level of 50 von. This means that this sound has a volume level of 50 background.
Isophone “0 background”, indicated by a dotted line, characterizes hearing threshold sounds of different frequencies for normal hearing.
In practice, what is often of interest is not the volume level expressed in backgrounds, but the value indicating how much louder a given sound is than another. Another interesting question is how the volumes of two different tones add up. So, if there are two tones of different frequencies with a level of 70 background each, this does not mean that the total volume level will be equal to 140 background.
The dependence of loudness on sound pressure level (and sound intensity) is a purely nonlinear curve; it has a logarithmic character. When the sound pressure level increases by 10 dB, the sound volume will increase by 2 times. This means that volume levels of 40, 50 and 60 von correspond to volumes of 1, 2 and 4 sones.
| Sound | Volume, sounds: |
Volume level, backgrounds: |
|---|---|---|
| Hearing threshold | 0 | 0 |
| The ticking of a wristwatch | ~ 0.02 | 10 |
| Whisper | ~ 0.15 | 20 |
| Wall clock sound | ~ 0.4 | 30 |
| Muffled conversation | ~ 1 | 40 |
| Quiet street | ~ 2 | 50 |
| Normal conversation | ~ 4 | 60 |
| Noisy street | ~ 8 | 70 |
| Health hazard level | ~ 10 | 75 |
| Pneumatic hammer | ~ 32 | 90 |
| Forge shop | ~ 64 | 100 |
| Loud music | ~ 128 | 110 |
| Pain threshold | ~ 256 | 120 |
| Siren | ~ 512 | 130 |
| Reactive plane | ~ 2048 | 150 |
| Lethal level | ~ 16384 | 180 |
| Noise weapon | ~ 65536 | 200 |
Notes
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2010.
See what “Sound Volume” is in other dictionaries: Physical encyclopedia
The magnitude of the auditory sensation, depending on the intensity of the sound and its frequency. At a constant frequency, the volume of a sound increases with increasing intensity. At the same intensity, the loudest sounds are in the frequency range 700-6000... ... Big Encyclopedic Dictionary
sound volume- The magnitude of the auditory sensation, depending on the intensity of the sound and its frequency [Terminological dictionary of construction in 12 languages (VNIIIS Gosstroy USSR)] Topics noise, sound EN sound loudnesssound volume DE Lautstärke FR intensité de sonvolume… … Technical Translator's Guide
The magnitude of the auditory sensation, depending on the intensity of the sound and its frequency. At a constant frequency, the volume of sound increases with increasing intensity. At the same intensity, the loudest sounds are in the frequency range 700... ... encyclopedic Dictionary
A measure of the strength of the auditory sensation caused by a sound. G. z. depends on the effective sound pressure and sound frequency (see figure). For comparison, G. z. use the value LN, called paradise. level of G. z. and is equal to: LN = 20 log(p*eff /p*0), where p*0 = 20... ... Big Encyclopedic Polytechnic Dictionary
sound volume- garsumas statusas T sritis radioelektronika atitikmenys: engl. volume of sound vok. Lautheit, f; Lautstärke, f; Tonstärke, f rus. sound volume, f pranc. volume sonore, m... Radioelektronikos terminų žodynas
A quantity characterizing the auditory sensation for a given sound. G. z. depends in a complex way on sound pressure (See Sound pressure) (or sound intensity (See Sound intensity)), frequency and shape of vibrations. With constant... ... Great Soviet Encyclopedia
sound volume- rus intensity (g) (strength) of sound, volume (g) of sound eng sound intensity fra intensité (f) acoustique, intensité (f) sonore, intensité (f) du son deu Schallintensität (f), Schallstärke (f) spa intensidad (f) sonora, intensidad (f) acústica … Occupational safety and health. Translation into English, French, German, Spanish
The magnitude of the auditory sensation, depending on the intensity of the sound and its frequency. At a constant frequency of G. z. increases with increasing intensity. At the same intensity, max. Sounds in the frequency range 700-6000 Hz are louder. Zero... ... Natural history. encyclopedic Dictionary
The magnitude of the auditory sensation, depending on the intensity of the sound and its frequency (Bulgarian language; Български) strength of sound (Czech language; Čeština) hlasitost zvuku (German language; Deutsch) Lautstärke (Hungarian language; Magyar) hangosság (Mongolian... ... Construction dictionary
Books
- Set of tables. Physics. Mechanical waves. Acoustics (8 tables), . Educational album of 8 sheets. Article - 5-8665-008. Wave process. Longitudinal waves. Transverse waves. Periodic waves. Wave reflection. Standing waves. Sound waves. Pitch of sound...
Power
By the word power in colloquial speech, many mean “power”, “strength”. Therefore, it is quite natural that buyers associate power with volume: “The more power, the better and louder the speakers will sound.” However, this popular belief is completely wrong! It is not always the case that a speaker with a power of 100 W will play louder or better than one that has a power rating of “only” 50 W. The power value rather speaks not about volume, but about the mechanical reliability of the acoustics. The same 50 or 100 W is not a sound volume at all, published by the column. Dynamic heads themselves have low efficiency and convert only 2-3% of the power of the electrical signal supplied to them into sound vibrations (fortunately, the volume of the sound produced is quite enough to create sound). The value indicated by the manufacturer in the passport of the speaker or the system as a whole only indicates that when a signal of the specified power is supplied, the dynamic head or speaker system will not fail (due to critical heating and interturn short circuit of the wire, “biting” of the coil frame, rupture of the diffuser , damage to flexible suspensions of the system, etc.).
Thus, the power of an acoustic system is a technical parameter, the value of which is not directly related to the loudness of the acoustics, although it is somewhat related to it. The rated power values of the dynamic heads, amplifier path, and speaker system may be different. They are indicated, rather, for orientation and optimal pairing between the components. For example, an amplifier of significantly lower or significantly higher power can damage the speaker in the maximum positions of the volume control on both amplifiers: on the first - due to the high level of distortion, on the second - due to the abnormal operation of the speaker.
Power can be measured in different ways and under different test conditions. There are generally accepted standards for these measurements. Let's take a closer look at some of them, most often used in the characteristics of products from Western companies:
RMS (Rated Maximum Sinusoidal power— set maximum sinusoidal power). Power is measured by applying a 1000 Hz sine wave until a certain level of harmonic distortion is reached. Usually in the product passport it is written like this: 15 W (RMS). This value indicates that the speaker system, when supplied with a 15 W signal, can operate for a long time without mechanical damage to the dynamic heads. For multimedia acoustics, higher power values in W (RMS) compared to Hi-Fi speakers are obtained due to measurements at very high harmonic distortion, often up to 10%. With such distortion, it is almost impossible to listen to the sound due to strong wheezing and overtones in the dynamic head and speaker body.
PMPO(Peak Music Power Output peak music power). In this case, power is measured by applying a short-term sine wave of less than 1 second duration and a frequency below 250 Hz (usually 100 Hz). In this case, the level of nonlinear distortions is not taken into account. For example, the speaker power is 500 W (PMPO). This fact suggests that the speaker system, after playing a short-term low-frequency signal, did not have any mechanical damage to the dynamic heads. Watt power units (PMPO) are popularly called “Chinese watts” due to the fact that power values using this measurement technique reach thousands of watts! Imagine - active speakers for a computer consume 10 VA electrical power from the AC mains and at the same time develop a peak musical power of 1500 W (PMPO).
Along with Western ones, there are also Soviet standards for various types of power. They are regulated by GOST 16122-87 and GOST 23262-88, which are still in force today. These standards define concepts such as rated, maximum noise, maximum sinusoidal, maximum long-term, maximum short-term power. Some of them are indicated in the passport for Soviet (and post-Soviet) equipment. Naturally, these standards are not used in world practice, so we will not dwell on them.
We draw conclusions: the most important in practice is the value of power indicated in W (RMS) at harmonic distortion (THD) values of 1% or less. However, comparison of products even by this indicator is very approximate and may have nothing to do with reality, because sound volume is characterized by sound pressure level. That's why information content of the indicator “speaker system power” zero.
Sensitivity
Sensitivity is one of the parameters indicated by the manufacturer in the characteristics of speaker systems. The value characterizes the intensity of the sound pressure developed by the speaker at a distance of 1 meter when a signal is supplied with a frequency of 1000 Hz and a power of 1 W. Sensitivity is measured in decibels (dB) relative to the hearing threshold (zero sound pressure level is 2*10^-5 Pa). Sometimes the designation used is the characteristic sensitivity level (SPL, Sound Pressure Level). In this case, for brevity, in the column with units of measurement, dB/W*m or dB/W^1/2*m is indicated. It is important to understand that sensitivity is not a linear proportionality coefficient between sound pressure level, signal power and distance to the source. Many companies indicate the sensitivity characteristics of dynamic drivers measured under non-standard conditions.
Sensitivity is a characteristic that is more important when designing your own speaker systems. If you do not fully understand what this parameter means, then when choosing multimedia acoustics for a PC, you can not pay special attention to the sensitivity (fortunately, it is not often indicated).
frequency response
Amplitude-frequency response (frequency response) in the general case is a graph showing the difference in the amplitudes of the output and input signals over the entire range of reproduced frequencies. The frequency response is measured by applying a sinusoidal signal of constant amplitude when its frequency changes. At the point on the graph where the frequency is 1000 Hz, it is customary to plot the 0 dB level on the vertical axis. The ideal option is in which the frequency response is represented by a straight line, but in reality such characteristics do not exist in acoustic systems. When considering the graph, you need to pay special attention to the amount of unevenness. The greater the unevenness value, the greater the frequency distortion of the timbre in the sound.
Western manufacturers prefer to indicate the range of reproduced frequencies, which is a “squeeze” of information from the frequency response: only the limiting frequencies and unevenness are indicated. Let's say it says: 50 Hz - 16 kHz (±3 dB). This means that this acoustic system has reliable sound in the range of 50 Hz - 16 kHz, but below 50 Hz and above 15 kHz the unevenness increases sharply, the frequency response has a so-called “blockage” (a sharp decline in the characteristics).
What does this mean? A decrease in the level of low frequencies implies a loss of richness and richness of the bass sound. The rise in the low-frequency region causes a sensation of booming and humming of the speaker. In the blockages of high frequencies, the sound will be dull and unclear. High frequencies indicate the presence of irritating, unpleasant hissing and whistling sounds. In multimedia speakers, the magnitude of the frequency response unevenness is usually higher than in so-called Hi-Fi acoustics. All advertising statements by manufacturers about the frequency response of speakers of the type 20 - 20,000 Hz (theoretical limit of possibility) should be treated with a fair amount of skepticism. At the same time, the unevenness of the frequency response is often not indicated, which can amount to unimaginable values.
Since manufacturers of multimedia acoustics often “forget” to indicate the unevenness of the frequency response of the speaker system, when encountering a speaker characteristic of 20 Hz - 20,000 Hz, you need to keep your eyes open. There is a high probability of buying a thing that does not even provide a more or less uniform response in the frequency band 100 Hz - 10,000 Hz. It is impossible to compare the range of reproduced frequencies with different irregularities.
Nonlinear distortion, harmonic distortion
Kg harmonic distortion factor. An acoustic system is a complex electroacoustic device that has a nonlinear gain characteristic. Therefore, the signal will necessarily have nonlinear distortion at the output after passing through the entire audio path. One of the most obvious and easiest to measure is harmonic distortion.
The coefficient is a dimensionless quantity. It is indicated either as a percentage or in decibels. Conversion formula: [dB] = 20 log ([%]/100). The higher the harmonic distortion value, the worse the sound usually is.
The kg of speakers largely depends on the power of the signal supplied to them. Therefore, it is stupid to make absentee conclusions or compare speakers only by harmonic distortion coefficient, without resorting to listening to the equipment. In addition, for the working positions of the volume control (usually 30..50%), the value is not indicated by the manufacturers.
Total electrical resistance, impedance
The electrodynamic head has a certain resistance to direct current, depending on the thickness, length and material of the wire in the coil (this resistance is also called resistive or reactive). When a music signal is applied, which is alternating current, the resistance of the head will change depending on the frequency of the signal.
Impedance(impedans) is the total electrical resistance to alternating current measured at a frequency of 1000 Hz. Typically the impedance of speaker systems is 4, 6 or 8 ohms.
In general, the value of the total electrical resistance (impedance) of an acoustic system will not tell the buyer anything related to the sound quality of a particular product. The manufacturer indicates this parameter only so that the resistance is taken into account when connecting the speaker system to the amplifier. If the speaker impedance value is lower than the recommended amplifier load value, the sound may be distorted or short-circuit protection will operate; if higher, the sound will be much quieter than with the recommended resistance.
Speaker housing, acoustic design
One of the important factors influencing the sound of an acoustic system is the acoustic design of the radiating dynamic head (speaker). When designing acoustic systems, the manufacturer usually faces the problem of choosing an acoustic design. There are more than a dozen species.
Acoustic design is divided into acoustically unloaded and acoustically loaded. The first implies a design in which the vibration of the diffuser is limited only by the rigidity of the suspension. In the second case, the oscillation of the diffuser is limited, in addition to the rigidity of the suspension, by the elasticity of the air and the acoustic resistance to radiation. Acoustic design is also divided into single and double acting systems. A single-action system is characterized by the excitation of sound traveling to the listener through only one side of the diffuser (the radiation from the other side is neutralized by the acoustic design). The double-acting system involves using both surfaces of the diffuser to produce sound.
Since the acoustic design of the speaker has virtually no effect on high-frequency and mid-frequency dynamic drivers, we will talk about the most common options for low-frequency acoustic design of the cabinet.
An acoustic scheme called a “closed box” is very widely applicable. Refers to a loaded acoustic design. It is a closed case with a speaker diffuser displayed on the front panel. Advantages: good frequency response and impulse response. Disadvantages: low efficiency, need for a powerful amplifier, high level of harmonic distortion.
But instead of having to deal with the sound waves caused by vibrations on the back of the diffuser, they can be used. The most common option among double-action systems is the bass reflex. It is a pipe of a certain length and cross-section mounted in a housing. The length and cross-section of the bass reflex are calculated in such a way that at a certain frequency, oscillations of sound waves are created in it, in-phase with the oscillations caused by the front side of the diffuser.
For subwoofers, an acoustic circuit commonly called a “resonator box” is widely used. Unlike the previous example, the speaker diffuser is not located on the housing panel, but is located inside, on the partition. The speaker itself does not directly participate in the formation of the low frequency spectrum. Instead, the diffuser only excites low-frequency sound vibrations, which then increase many times in volume in the bass reflex pipe, which acts as a resonant chamber. The advantage of these design solutions is high efficiency with small dimensions of the subwoofer. Disadvantages manifest themselves in deterioration of phase and impulse characteristics, the sound becomes tiring.
The optimal choice would be medium-sized speakers with a wooden body, made in a closed circuit or with a bass reflex. When choosing a subwoofer, you should pay attention not to its volume (even inexpensive models usually have sufficient reserve for this parameter), but to reliable reproduction of the entire low frequency range. In terms of sound quality, speakers with thin bodies or very small sizes are the most undesirable.
Sound waves are characterized by propagation speed, sound pressure, intensity, spectral composition and a number of other quantities.
To form units of acoustics, as well as mechanics, three basic units are sufficient: length L, masses M and time T. Typically, acoustics uses the SI system of units. At the same time, in practice, non-systemic units are also used (decibel, background, octave, atmosphere, etc.) We list here only some of the frequently used acoustic quantities.
Speed sound- the phase speed of sound waves in an elastic medium, usually the same for all frequency components of sound. Expressed in meters per second ( m/s). The speed of sound in air at a temperature of 0 C and a pressure of 1 atm (101325 Pa) is 331 m/s.
Sound pressure R- the variable part of the pressure that occurs when a sound wave passes through a medium. Propagating in a medium, a sound wave forms its condensations and rarefactions, which create additional pressure changes in relation to its average values in the medium.
Sound pressure is the variable part of pressure, i.e. pressure fluctuations around the average value, the frequency of which corresponds to the frequency of the sound wave. Sound pressure -- main quantitative characteristic sound.
Sound pressure, like any pressure, is measured in pascals ( 1Pa = 1 newton on m 2 ) and has the dimension LMT. Sometimes the sound pressure level is used to characterize sound -- expressed in db ratio of the magnitude of a given sound pressure R to the threshold sound pressure value R O =2·10 -5 n/m 2 . In this case, the number of decibels N=20 lg (p/p o ).
Sound pressure in the air varies widely - from 10 -5 n/m 2 close to the hearing threshold 10 3 n/m 2 at the loudest sounds, such as jet aircraft.
At significant sound pressure, the phenomenon of discontinuity of liquid continuity is observed - cavitation.
Sound pressure must be distinguished from radiation pressure sound.
Sound pressure is the most important characteristic of sound, because of all acoustic quantities, the human ear perceives, first of all, sound pressure.
Acoustic radiation pressure(sound radiation pressure) - constant pressure experienced by a body located in a stationary sound field. Sound radiation pressure should not be confused with sound pressure, which is a periodically changing pressure in the medium in which the sound wave propagates.
Sound pressure is proportional to the density of sound energy and therefore the square of the sound pressure. It few By comparison with sound pressure; so, for example, in a sound field in air, in which the sound pressure is 10 2 n/m 2 , with normal incidence of a sound wave on an obstacle that completely reflects sound, the sound pressure is approximately equal to 0.1 n/m 2 . Radiation sound pressure is measured radiometer. Knowing the sound pressure value, you can determine the absolute value intensity sound in this environment.
Sound energy W- the energy of vibrational motion of particles of an elastic medium filling the sound field region. Like any other energy, sound energy is expressed in joules ( j) and has the dimension LMT.
Density sound energy w=dW/dV has dimension LMT and unit of measurement j/m.
Flow sound energy P=dW/dt, as well as sound power P=dW/dt- all these energy quantities are expressed in watts ( W) and has the dimension LMT.
Intensity sound(sound power density), also called sound intensity, - time-average energy transferred by a sound wave through a unit area perpendicular to the direction of propagation of the wave per unit time: I=dР/dS, has dimension MT.
For a plane sinusoidal traveling wave, the sound intensity
I = pv/2 = p 2 /2rc,
Where R-- amplitude of sound pressure, v-- amplitude vibrational speed, r-- density of the medium, With- the speed of sound in it. In a spherical traveling wave, the sound intensity is inversely proportional to the square of the distance from the source. In a standing wave I = 0 , i.e., there is no flow of sound energy on average.
Sound intensity is measured in SI units in W/M 2 . Sound intensity is also measured by intensity level on the decibel scale; decibel number
N = 10 lg (I/I 0 ) ,
Where I-- intensity of a given sound, I 0 = 10 -12 W/M 2 .
Intensity sound and is expressed in watts per square meter ( W/m).
Acoustic resistance- a physical quantity similar to the resistance of an electrical circuit. Has dimension LMT and is expressed in pascal seconds per cubic meter.
Range sound- frequency response of sound, describing its spectral composition in relation to some acoustic quantity (usually sound pressure, sound intensity, etc.). As a rule, in acoustic practice one has to deal with continuous spectra, when the energy of sound vibrations is distributed continuously over a certain frequency range. At the same time, when solving certain problems (calibration, reception and transmission of calibration signals, etc.), there is a need to use linear - discrete frequency components of the spectrum.
Some acoustic quantities associated with human perception of sound (sound intensity, sound pressure, attenuation of sound waves, etc.) have an exponential change and, as a result, can vary in value over a very wide range - by several orders of magnitude.
In turn, the human ear has a huge range of susceptibility: it catches the quietest rustle of foliage and at the same time withstands shaking thunderclaps. This ability of human auditory perception is described in the empirical psychophysiological law of Weber-Fechner as follows: sensation is proportional to the logarithm of irritation.
If the impact increases by 10 times, its tenth logarithm increases by one and the sensation also increases by some unit. And when the impact increases by a million times, its logarithm, and at the same time the sensation, increases by only six of the same units. An important conclusion follows from this fact: the psychophysiological law determines the change in the amplitude and frequency of perceived sounds over such a wide range that it is practically impossible to use linear scales and it is necessary to resort to a logarithmic scale. But this same law makes the use of logarithmic quantities and their units in acoustics quite natural.
The relative level of an acoustic quantity using a logarithmic scale is defined as the logarithm of the ratio of a given value X values to the threshold (initial) value X this value. taken as the starting point:
level quantities = lg X/X .
For example, the sound intensity level is the decimal logarithm of the ratio of a given sound intensity value I to the threshold value I sound intensity .
The relative level is indicated by the letter L with an index indicating the type of acoustic quantity, for example Lp- sound pressure level. The following are taken as initial levels:
- o sound pressure level - 20 µPa;
- o sound power level - 10 -12 W;
- o sound intensity level - 0.01 W/m2.
If it is necessary to indicate the original value, its value is placed in parentheses after the designation of the logarithmic value and the letters re (the initial letters of the word referens). For example, for sound pressure level L p (re 20 μPa) = 20 dB.
When using logarithmic quantities for the magnitude level, the base of the logarithms (ten, square root of ten, two, etc.), the threshold value of the magnitude, and the parameter itself (sound pressure level, sound intensity level, etc.) are indicated. To quantify levels and other logarithmic quantities, the units of bel and decibel are used.
Bel has two different meanings: one with a logarithmic base of ten, and the second with a base of ten. The decimal base of the logarithm is used for energy quantities, and the base is used for force quantities.
Bel(B) there is an increase in energy quantity (sound power R, energy W, intensity I or other energy value) 10 times:
1 white = log (P 2 / P 1) at P 2 = 10 P 1. (1.2.1)
Since energy quantities are proportional to the squares of force quantities (sound pressure, electric current, etc.), bel also represents an increase in force quantity by a factor of = 3.162.
However, in practice, it is not the bel that is most widely used, but its submultiple unit - the decibel (dB): 1dB = 0.1 B.
Decibel corresponds to a change in the energy value by 10 0.1 = = 1.259 times or the force value by = 1.121 times. There is also an independent definition of decibel: decibel - sound pressure level R, for which the relation 20 lg (p/p 0) = 1 is satisfied, where p 0 is the threshold sound pressure equal to 20 μPa.
Sound power is the amount of sound energy emitted per unit time in watts.
Level sound power- logarithm of the ratio of a given sound power to the original sound power. The sound power level in decibels is equal to ten times the logarithm with a base of ten of this ratio:
Lp = 10 lg(P/P 0),
where P sound power, W, P 0 threshold sound power, P 0 = 10 -12 W = 1 pW, unless otherwise indicated.
Since the power of an acoustic signal is proportional to the square of its amplitude (sound power is proportional to the square of the amplitude of sound pressure), then an increase in the signal amplitude of one bel corresponds to the value
One decibel corresponding to a change in amplitude in at 10 times is a relatively small value. Therefore in decibels
If A(u) was the ratio of powers, then the logarithm on the right side of (1.2.2) should have a factor of 10. Since A(u) is the ratio not of powers, but of output and input quantities (displacements, speeds, voltages, currents, etc.), then an increase in this ratio by ten times will correspond to an increase in the power ratio by a hundred times, which corresponds to two bels or twenty decibels. Therefore, on the right side of (1.2.2) there is a factor of 20.
Level intensity sound(sound pressure flux density level) - the logarithm of the ratio of a given sound intensity in a specified direction to the original intensity. The intensity level in decibels is equal to ten times the logarithm with a base of ten of this ratio. Unless otherwise indicated, the initial sound intensity is taken to be 1 pW/m2.
Level sound pressure- logarithm of the ratio of a given sound pressure to the original sound pressure. The sound pressure level in decibels is equal to twenty logarithms of this ratio with a base of ten. Unless otherwise indicated, the initial sound pressure in air is taken to be 20 μPa and 1 μPa in other media, and it is assumed that sound pressures are expressed in terms of root mean square values.
In addition to objective acoustic characteristics, there are also subjective sound characteristics that characterize a person’s auditory perception of sounds. These include: sound volume, hearing threshold, pain threshold and others.
Volume sound- a quantity characterizing the level of auditory sensation of sound. The volume of sound depends in a complex way on sound pressure (sound intensity), on the frequency and shape of sound vibrations. With a constant frequency and shape of vibrations, the volume of sound increases with increasing sound pressure. A person is most sensitive to sounds in the frequency range 1 - 5 kHz.
The loudness of a sound of a given frequency is assessed by comparing it with the loudness of a pure tone with a frequency of 1000 Hz, introducing for this the logarithmic value “loudness level”. The volume level is assessed in backgrounds.
Background there is a volume level for which the sound pressure level of an equally loud sound of a standard pure tone with a frequency of 1000 Hz is equal to 1 dB. For a standard tone, the volume level in the phons is the same as the sound pressure level in decibels.
Threshold audibility- sound pressure at which the weakest sounds of a given frequency are heard. The lowest hearing threshold corresponds to frequencies in the range 1 - 5 G kHz.
Threshold painful Feel- sound pressure at which normal auditory sensation turns into painful irritation of the hearing organs. In the frequency range 1 - 5 kHz, the pain threshold is about 120 dB.
Key words : speed sound, sound pressure, density sound energy, flow sound energy, intensity sound, acoustic resistance, range sound, psychophysiological law, level acoustic quantities, logarithmic size, logarithm, white, decibel, volume, threshold audibility, threshold painful Feel.
Control questions
- 1. Specify range sound waves
- 2. List acoustic quantities And please indicate unit measurements.
- 3. What such range sound?
- 4. IN how consists of psychophysiological law Weber-Fechner?
- 5. Why V acoustics expedient use logarithmic magnitude?
- 6. What such relative level acoustic magnitude?
- 7. What such white?
- 8. What such decibel And How He connected With white?
- 9. Give definition level sound power, level intensity sound, level sound pressure.
- 10. What such volume sound?
- 11. What such threshold audibility?
- 12. What such threshold painful Feel?
In the article you will learn what sound is, what its lethal volume level is, as well as its speed in the air and other media. We’ll also talk about frequency, encoding and sound quality.
We will also consider sampling, formats and sound power. But first, let's define music as ordered sound - the opposite of disordered, chaotic sound, which we perceive as noise.
- These are sound waves that are formed as a result of vibrations and changes in the atmosphere, as well as objects around us.
Even when talking, you hear your interlocutor because he influences the air. Also, when you play a musical instrument, whether you beat a drum or pluck a string, you produce vibrations of a certain frequency, which produces sound waves in the surrounding air.
There are sound waves ordered And chaotic. When they are ordered and periodic (repeated after a certain period of time), we hear a certain frequency or pitch of sound.
That is, we can define frequency as the number of times an event occurs in a given period of time. Thus, when sound waves are chaotic, we perceive them as noise.
But when the waves are ordered and repeat periodically, then we can measure them by the number of repeating cycles per second.
Audio sampling rate
The audio sampling rate is the number of signal level measurements per second. Hertz (Hz) or Hertz (Hz) is a scientific unit of measurement that determines the number of times an event occurs per second. This is the unit we will use!
Audio sampling rate You've probably seen this abbreviation very often - Hz or Hz. For example, in equalizer plugins. Their units of measurement are hertz and kilohertz (that is, 1000 Hz).
Typically, a person hears sound waves from 20 Hz to 20,000 Hz (or 20 kHz). Anything less than 20 Hz is infrasound. Anything above 20 kHz is ultrasound.
Let me open the equalizer plugin and show you what it looks like. You are probably familiar with these numbers.
Sound frequencies With an equalizer, you can cut or boost certain frequencies within the human audible range.
A small example!
Here I have a recording of a sound wave that was generated at a frequency of 1000 Hz (or 1 kHz). If we zoom in and look at its shape, we will see that it is regular and repeating (periodic).
Repetitive (periodic) sound wave In one second, a thousand repeating cycles occur here. For comparison, let's look at a sound wave, which we perceive as noise.
Disordered sound There is no specific repeating frequency here. There is also no specific tone or pitch. The sound wave is not ordered. If we look at the shape of this wave, we can see that there is nothing repeating or periodic about it.
Let's move on to the richer part of the wave. We zoom in and see that it is not constant.
Disordered wave when scaling Due to the lack of cyclicity, we are not able to hear any specific frequency in this wave. Therefore we perceive it as noise.
Lethal sound level
I would like to mention a little about the lethal sound level for humans. It originates from 180 dB and higher.
It is worth saying right away that according to regulatory standards, a safe noise level is considered to be no more than 55 dB (decibels) during the day and 40 dB at night. Even with prolonged exposure to hearing, this level will not cause harm.
| Sound volume levels | ||
|---|---|---|
| (dB) | Definition | Source |
| 0 | It's not loud at all | |
| 5 | Almost inaudible | |
| 10 | Almost inaudible | Quiet rustling of leaves |
| 15 | Barely audible | rustling leaves |
| 20 — 25 | Barely audible | Whisper of a person at a distance of 1 meter |
| 30 | Quiet | Wall clock ticking ( permissible maximum according to standards for residential premises at night from 23 to 7 o'clock) |
| 35 | Quite audible | Muffled conversation |
| 40 | Quite audible | Ordinary speech ( norm for residential premises during the day from 7 to 23 hours) |
| 45 | Quite audible | Talk |
| 50 | Clearly audible | Typewriter |
| 55 | Clearly audible | Talk ( European standard for class A office premises) |
| 60 | (the norm for offices) | |
| 65 | Loud conversation (1m) | |
| 70 | Loud conversations (1m) | |
| 75 | Scream and laughter (1m) | |
| 80 | Very noisy | Scream, motorcycle with muffler |
| 85 | Very noisy | Loud scream, motorcycle with muffler |
| 90 | Very noisy | Loud screams, freight railway car (7m) |
| 95 | Very noisy | Subway car (7 meters outside or inside the car) |
| 100 | Extremely noisy | Orchestra, thunder ( according to European standards, this is the maximum permissible sound pressure for headphones) |
| 105 | Extremely noisy | On old planes |
| 110 | Extremely noisy | Helicopter |
| 115 | Extremely noisy | Sandblasting machine (1m) |
| 120-125 | Almost unbearable | Jackhammer |
| 130 | Pain threshold | Airplane at the start |
| 135 — 140 | Contusion | Jet plane taking off |
| 145 | Contusion | Rocket launch |
| 150 — 155 | Concussion, injuries | |
| 160 | Shock, trauma | Shock wave from a supersonic aircraft |
| 165+ | Rupture of eardrums and lungs | |
| 180+ | Death | |
Speed of sound in km per hour and meters per second
The speed of sound is the speed at which waves propagate in a medium. Below I give a table of propagation speeds in various environments.
The speed of sound in air is much less than in solid media. And the speed of sound in water is much higher than in air. It is 1430 m/s. As a result, propagation is faster and audibility is much further.
Sound power is the energy that is transmitted by a sound wave through the surface under consideration per unit time. Measured in (W). There is an instantaneous value and an average (over a period of time).
Let's continue working with the definitions from the music theory section!
Pitch and note
Height is a musical term that means almost the same thing as frequency. The exception is that it does not have a unit of measurement. Instead of defining sound by the number of cycles per second in the range of 20 - 20,000 Hz, we designate certain frequency values using Latin letters.
Musical instruments produce regular, periodic sound waves that we call tones or notes.
That is, in other words, it is a kind of snapshot of a periodic sound wave of a certain frequency. The pitch of this note tells us how high or low the note sounds. In this case, lower notes have longer wavelengths. And the tall ones are shorter.
Let's look at a 1 kHz sound wave. Now I'll zoom in and you'll see the distance between the loops.
Sound wave at 1 kHz Now let's look at a 500 Hz wave. Here the frequency is 2 times less and the distance between cycles is greater.
Sound wave at 500 Hz Now let's take a wave of 80 Hz. It will be even wider here and the height will be much lower.
Sound at 80 Hz We see the relationship between the pitch of a sound and its waveform.
Each musical note is based on one fundamental frequency (fundamental tone). But in addition to tone, music also consists of additional resonant frequencies or overtones.
Let me show you another example!
Below is a wave at 440 Hz. This is the standard in the world of music for tuning instruments. It corresponds to the note A.
Pure sound wave at 440 Hz We hear only the fundamental tone (pure sound wave). If we zoom in, we will see that it is periodic.
Now let's look at a wave of the same frequency, but played on a piano.
Intermittent piano sound Look, it is also periodic. But it has small additions and nuances. All of them together give us an idea of how a piano sounds. But besides this, overtones also determine the fact that some notes will have a greater affinity for a given note than others.
For example, you can play the same note, but an octave higher. It will sound completely different. However, it will be related to the previous note. That is, it is the same note, only played an octave higher.
This relationship between two notes in different octaves is due to the presence of overtones. They are constantly present and determine how closely or distantly certain notes are related to each other.
