Rice. Fig. 2. Change in the ratio of the reference frequencies of biological and social time In the upper part of fig. Figure 2 conventionally shows the total duration of the global historical process (the time scale is conditional, uneven). Below are two axes of time. On them

The process of transferring vibrations in a medium is called wave.

Rice. 1 Wave motion

The main characteristic of wave motion is the wavelength, the so-called. the distance between two points on a wave that are in the same phase. Another characteristic is the amplitude of the wave - the distance by which the oscillating particle deviates from the equilibrium position.

The wave motion is also characterized by the frequency f this movement and the speed of propagation.

Frequency - the number of oscillations per unit of time (usually per second, s), measured in hertz, Hz.

The frequency of sound waves perceived by a normal human ear ranges from 16 to 16,000 Hz. Oscillations with a frequency of less than 16 Hz are called infrasound, more than 16,000 Hz - ultrasound.

Rice. 2[__] Frequency in octave intervals

Sound how a physical phenomenon is a wave motion of an elastic medium; as a physical phenomenon, it appears as a sensation perceived by the organ of hearing when exposed to sound waves in the frequency range of 16-16000 Hz. In other words sound called the mechanical vibrations of an elastic body in the frequency range of human hearing.

The process of distribution of oscillatory motion in a medium is called sound wave. The region of the medium in which sound waves propagate is called sound field.

Sound waves, like any wave motion, are characterized by a wavelength λ in m, a frequency f in hertz, Hz, and oscillation period T in seconds, s, as well as the speed of their propagation FROM in m/s.

The relationship between these quantities can be represented as follows:

λ \u003d C / f \u003d C T (1)

If the displacement of the particles of the medium occurs in the direction of propagation of the sound wave, then such waves are called longitudinal. In air and liquids, sound propagates only in the form of longitudinal waves. In solids, along with longitudinal waves, the formation of transverse and bending waves occurs.

In order to analyze the sound field, the sound range (16-16000 Hz) is divided into bands (intervals, steps).

Octave band - the frequency range in which the upper cutoff frequency f 2 twice the bottom f 1 .

One-third octave frequency band - the frequency range in which this ratio is 1.26 ( f 2 = 1,26 f one). Octave and one-third octave bands are characterized by the geometric mean frequency of the band

(2)

The boundary and geometric mean frequencies of the octave and one-third octave bands are given in Table. P1.

Table A.1

Boundary and geometric mean

frequencies of octave and one-third octave bands, Hz

For air, the dependence of velocity on temperature looks like:

FROM = 331,4 + 0,6t, m/s (3)

where 331.4 is the speed of sound in air at 0ºС;

t– ambient temperature, ºС.

Table 1

The speed of sound in various materials

If we take the average speed of sound in air as 340 m/s, then we can get a frequency-dependent wavelength.

The change in the state of the medium in the sound field is characterized by the sound pressure p and the oscillatory velocity of the particles of the medium V.

Sound pressure p is the difference between the instantaneous value of the total pressure and the average (atmospheric) pressure, which is observed in the medium in the absence of a sound field. The unit of measurement of sound pressure p is N / m 2, 1 N / m 2 \u003d 1 Pa (Pascal).

The oscillatory speed of the particles of the medium V called the instantaneous value of the speed of the oscillatory motion of the particles of the medium during the propagation of a sound wave in it. The oscillatory speed of the particles of the medium is a vector quantity, the unit of measurement is m/s.

The relationship between these physical quantities in a plane traveling wave is determined by the relation

p = Vρс, (4)

where ρ is the density of the medium. The value ρс - constant for a given medium - is called acoustic (wave) resistance and for air under normal atmospheric conditions (р = 10 5 Pa, t = 20°С) ρс = 408 Pa·s/m.

The propagation of a sound wave is accompanied by the transfer of energy. The average flow of sound energy passing per unit time through a unit surface normal to the propagation of a sound wave is called the sound intensity I, which is measured in W / m 2. The relationship between sound pressure and sound intensity in a traveling wave is established by the relation:

, (5)

where the bar means time averaging.

Another energy characteristic of the sound field is the sound energy density ω in J/m 3 , which is equal to the amount of sound energy contained in a unit volume.

For plane sound waves, it is determined by the relation

Sound intensity is a vector, and sound energy density is a scalar quantity.

A person perceives sound only in certain intervals. The minimum value of sound pressure that a person perceives as sound is called the hearing threshold (p 0 = 2 10 -5 Pa). The maximum value of sound pressure that a person perceives without the risk of hearing damage is called the pain threshold (p = 2 10 2 Pa). The hearing threshold corresponds to sounds with intensity I 0 = 10 -12 W / m 2, and the pain threshold - I = 10 2 W / m 2.

The concept of the so-called level is introduced, in which absolute values ​​are taken in relation to certain values ​​(at the threshold of hearing), and this ratio is logarithmic. The unit of measure is the decibel (dB). In this way, decibel is a number that expresses the ratio of two quantities on a logarithmic scale.

Sound intensity level, dB,

Sound pressure level, dB,

Rice. 3 The area of ​​​​human auditory perception of sound

Since the decibel is a logarithmic value, arithmetic operations with it have their own characteristics, for example:

L 1 + L 2 \u003d 70 dB + 70 dB \u003d 10lg (10 0.1 70 + 10 0.1 70) \u003d

10lg (10 7 + 10 7) \u003d 10lg (2 10 7) \u003d 10 7.3 \u003d 73 dB

The decibel addition formula is:

L 1 + L 2 \u003d 10lg (10 0.1 L 1 + 10 0.1 L 2)

In general terms, in the presence of several sound sources, the total sound pressure levels are determined by the formula

, (9)

where L i are the terms of sound pressure levels, dB;

n is the total number of terms.

L = L 1 + ΔL (L 1 > L 2) (10)

Example. It is required to find the total levels for three terms: L 1 = 86 dB; L 2 = 80 dB; L 3 = 88 dB. Difference ΔL 3.1 =2 dB; correction ΔL 1 =2 dB; L 3.1 = 90 dB; L 3.1 - L 2 \u003d 10 dB, correction ΔL 2 \u003d 0.4 dB; L 3,1,2 = 90.4 dB.

Instruments for measuring noise are called sound level meters. These devices consist of a microphone, an amplifier and a measuring device with scales. A, B, C and D. A complete characterization of noise can be obtained by measuring the sound pressure level on a scale FROM and its frequency response (distribution of noise components by frequency and sound pressure level). In order to bring the measurement results closer to the subjective perception of a person, the concept of a corrected sound pressure level has been introduced. The most commonly used sound level meter correction BUT.

Rice. four BUT sound level meter

The standard correction value ΔL A is given below

Corrective sound pressure level

L A \u003d L - ΔL A (11)

called the sound level in dBA.

Thus, the definition of sound levels in dBA is the following - this is the energy sum of octave sound pressure levels in the normalized frequency range, corrected for the frequency response BUT sound level meter.

An example of determining the sound level in dBA

Basic concepts and definitions. Auditory perception as a means of obtaining information is the second most important (after visual) psychophysiological process for a person.

Noise- any sound that is undesirable for a person. Sound waves excite vibrations of the particles of the sound medium, as a result of which atmospheric pressure changes.

Sound pressure is the difference between the instantaneous pressure value at a point in the medium and the static pressure at the same point, i.e. pressure in an undisturbed medium: P \u003d R mg - R st .

Sound pressure is a sign-variable quantity. At the moments of condensation (compression or compaction) of the particles of the medium, it is positive; at the moments of rarefaction - negative.

The organs of hearing perceive not instantaneous, but root-mean-square sound pressure:

Pressure averaging time: T o = 30 - 100 ms.

When a sound wave propagates, energy transfer.

The average energy flux at a point in a medium per unit time, per unit surface, normal to the direction of wave propagation, is called sound intensity (strength of sound) at this point.

The intensity, W / m 2, is related to the sound pressure dependence

where ρ×s– specific acoustic impedance.

The values ​​of sound pressure and sound intensity, which have to be dealt with in the practice of noise control, can vary over a wide range: in pressure - up to 10 8 times, in intensity - up to 10 16 times. It is somewhat inconvenient to operate with such figures.

In addition, the auditory analyzer obeys the basic psychophysical law (Weber-Fechner):

where E- the intensity of sensations; I is the intensity of the stimulus; FROM and To are some constants.

Therefore, they introduced logarithmic quantities sound pressure level and sound intensity.

Sound pressure level, dB:

where R o= 2×10 -5 Pa – threshold sound pressure; R is the root-mean-square value of the sound pressure.

Sound intensity level, dB:

where I is the effective sound intensity; I o\u003d 10 -12 W / m 2 - sound intensity corresponding to the threshold of hearing (at a frequency of 1000 Hz).

The value of the intensity level is used in obtaining formulas for acoustic calculations, and the sound pressure level is used to measure noise and assess its impact on a person, since the hearing organ is sensitive not to intensity, but to RMS pressure.

Intensity Imax and sound pressure value Pmax corresponding to the pain threshold: Imax= 10 2 W/m, Pmax\u003d 2 × 10 2 Pa.

Noise frequency spectrum– dependence of the intensity level (sound pressure level) on frequency: L = L(ƒ). The entire audible frequency range is divided into 9 octave bands. Octave band, or octave is the frequency range for which the condition

There are the following types of spectra:

- discrete (linear)- a spectrum, the sinusoidal components of which are separated from each other in frequency (Fig. 6.1);

Octave band - a frequency band in which the upper cut-off frequency fv is equal to twice the lower frequency fn, i.e. fv / fn \u003d 2.

The octave band is characterized by the geometric mean frequency fСГ:

fv=2* fn=357*2=714 Hz

Answer: the upper limit frequency is 714 Hz, the lower limit frequency is 357 Hz.

2.4 Electromagnetic fields and radiation

It is believed that electromagnetic radiation with a wavelength of 20-30 cm is the most harmful to the human body. What is the frequency of these waves? What parameters are normalized for this range?

The wave frequency is determined by the following formula:

c is the speed of light in vacuum ;

is the wavelength,

Determine the wave frequencies for the extreme points of the wavelength range :

Thus, we obtain that for the wavelength range corresponds to the following frequency range .

The effective value of the electric field strength, measured at a distance of 1 m from the TV screen, turned out to be equal to E V/m. Distance protection is an effective way to protect against electromagnetic radiation. Assuming that the intensity E decreases with distance

proportionally to the cube, to determine at what distance the accepted by a number of researchers as a safe value Edop. = 0.5 V / m will be measured? What is E at a distance of x = 2 m and at a distance of 4 m recommended by hygienists?

Since the intensity E decreases with distance in proportion to the cube, we determine at what distance the accepted by a number of researchers as a safe value Edop. = 0.5 V / m will be measured:

We also determine the tension E at various distances from the TV screen:

And in conclusion, we determine the tension E at the recommended TV viewing distance:

Thus, we get that the tension decreases with increasing distance from the radiation source, in this case, the TV. The most recommended distance r = 4 m is preferable, as it is the best option, which provides the most comfortable TV viewing, and there is also a small value of the operating voltage.