Occurring in gaseous, liquid and solid media, which, upon reaching the human hearing organs, is perceived by him as sound. The frequency of these waves ranges from 20 to 20,000 vibrations per second. Let us give formulas for a sound wave and consider in more detail its properties.

Why is there a sound wave?

Many people wonder what a sound wave is. The nature of sound lies in the appearance of a disturbance in an elastic medium. For example, when a pressure disturbance in the form of compression occurs in a certain volume of air, then this area tends to spread in space. This process leads to compression of air in areas adjacent to the source, which also tend to expand. This process covers more and more of the space until it reaches some kind of receiver, for example, the human ear.

General characteristics of sound waves

Consider the questions of what a sound wave is and how it is perceived by the human ear. The sound wave is longitudinal; when it enters the concha, it causes the ear membrane to vibrate with a certain frequency and amplitude. It is also possible to represent these fluctuations as periodic changes in pressure in a micro-volume of air adjacent to the membrane. First, it increases relative to normal atmospheric pressure, and then decreases, obeying the mathematical laws of harmonic motion. The amplitude of changes in air compression, that is, the difference between the maximum or minimum pressure created by a sound wave with atmospheric pressure is proportional to the amplitude of the sound wave itself.

Many physical experiments have shown that the maximum pressures that the human ear can perceive without harming it is 2800 μN / cm 2. For comparison, let's say that the atmospheric pressure near the earth's surface is 10 million μN / cm 2. Taking into account the proportionality of pressure and amplitude of oscillations, we can say that the latter value is insignificant even for the strongest waves. If we talk about the length of a sound wave, then for a frequency of 1000 vibrations per second, it will be a thousandth of a centimeter.

The weakest sounds create pressure fluctuations of the order of 0.001 µN / cm 2, the corresponding wave amplitude for a frequency of 1000 Hz is 10 -9 cm, while the average diameter of air molecules is 10 -8 cm, that is, the human ear is an extremely sensitive organ.

The concept of the intensity of sound waves

From a geometric point of view, a sound wave is vibrations of a certain shape, from a physical point of view, the main property of sound waves is their ability to transfer energy. The most important example of wave energy transfer is the sun, whose radiated electromagnetic waves provide energy to our entire planet.

The intensity of a sound wave in physics is defined as the amount of energy carried by a wave through a unit of surface that is perpendicular to the propagation of the wave, and per unit of time. In short, the intensity of a wave is its power transferred across a unit area.

The strength of sound waves is usually measured in decibels, which are based on a logarithmic scale that is convenient for practical analysis of the results.

The intensity of various sounds

The following decibel scale gives an idea of \u200b\u200bthe meaning of the various and the sensations it causes:

• the threshold of unpleasant and uncomfortable sensations starts from 120 decibels (dB);
• the riveting hammer generates 95 dB noise;
• high-speed train - 90 dB;
• street with heavy car traffic - 70 dB;
• the volume of a normal conversation between people - 65 dB;
• a modern car moving at moderate speeds generates a noise of 50 dB;
• average radio volume - 40 dB;
• quiet conversation - 20 dB;
• tree foliage noise - 10 dB;
• the minimum threshold of human sound sensitivity is close to 0 dB.

The sensitivity of the human ear depends on the frequency of sound and is the maximum value for sound waves with a frequency of 2000-3000 Hz. For sound in this frequency range, the lower threshold of human sensitivity is 10 -5 dB. Higher and lower frequencies than the specified interval lead to an increase in the lower threshold of sensitivity in such a way that a person hears frequencies close to 20 Hz and 20,000 Hz only when their intensity is several tens of dB.

As for the upper threshold of intensity, after which the sound begins to cause inconvenience for a person and even painful sensations, it should be said that it practically does not depend on the frequency and lies in the range of 110-130 dB.

Geometric characteristics of a sound wave

A real sound wave is a complex oscillatory packet of longitudinal waves that can be decomposed into simple harmonic oscillations. Each such vibration is described from a geometric point of view by the following characteristics:

1. Amplitude is the maximum deviation of each section of the wave from equilibrium. For this value, the designation A.
2. Period. This is the time during which a simple wave makes its full swing. After this time, each point of the wave begins to repeat its own oscillatory process. The period is usually denoted by the letter T and measured in seconds in the SI system.
3. Frequency. This is a physical quantity that shows how many vibrations a given wave makes per second. That is, in its meaning, it is the reciprocal of the period. It is designated f. For the frequency of a sound wave, the formula for determining it through a period is as follows: f \u003d 1 / T.
4. The wavelength is the distance that it travels in one period of oscillation. Geometrically, wavelength is the distance between two closest highs or two closest lows on a sinusoidal curve. The oscillation length of a sound wave is the distance between the nearest areas of air compression or the closest places of its rarefaction in the space where the wave moves. It is usually denoted by the Greek letter λ.
5. The speed of propagation of a sound wave is the distance over which the region of compression or the region of discharge of the wave extends per unit time. This value is designated by the letter v. For the speed of a sound wave, the formula is: v \u003d λ * f.

The geometry of a pure sound wave, that is, a wave of constant purity, obeys a sinusoidal law. In general, the formula for a sound wave is: y \u003d A * sin (ωt), where y is the value of the coordinate of a given point of the wave, t is time, ω \u003d 2 * pi * f is the cyclic oscillation frequency.

Aperiodic sound

Many sound sources can be considered periodic, for example, the sound from musical instruments such as a guitar, piano, flute, but there are also a large number of sounds in nature that are aperiodic, that is, sound vibrations change their frequency and shape in space. Technically, this kind of sound is called noise. Prominent examples of aperiodic sound are city noise, the noise of the sea, sounds from percussion instruments, for example, from a drum, and others.

Sound wave propagation medium

Unlike electromagnetic radiation, the photons of which do not need any material medium for their propagation, the nature of sound is such that a certain medium is needed for its propagation, that is, according to the laws of physics, sound waves cannot propagate in a vacuum.

Sound can propagate in gases, liquids and solids. The main characteristics of a sound wave propagating in a medium are as follows:

• the wave propagates linearly;
• it propagates equally in all directions in a homogeneous medium, that is, the sound diverges from the source, forming an ideal spherical surface.
• regardless of the amplitude and frequency of sound, its waves propagate at the same speed in a given environment.

The speed of sound waves in various environments

The speed of sound propagation depends on two main factors: on the medium in which the wave travels and on temperature. In general, the following rule applies: the denser the medium is, and the higher its temperature, the faster sound moves in it.

For example, the speed of propagation of a sound wave in air near the earth's surface at a temperature of 20 ℃ and a humidity of 50% is 1235 km / h or 343 m / s. In water, at a given temperature, sound moves 4.5 times faster, that is, about 5735 km / h or 1600 m / s. As for the dependence of the speed of sound on the temperature in air, it increases by 0.6 m / s with an increase in temperature for each degree Celsius.

Timbre and tone

If a string or metal plate is allowed to vibrate freely, it will produce sounds of different frequencies. It is very rare to find a body that would emit a sound of one specific frequency, usually the sound of an object has a set of frequencies in a certain interval.

The timbre of a sound is determined by the number of harmonics present in it and their respective intensities. Timbre is a subjective value, that is, the perception of a sounding object by a specific person. Timbre is usually characterized by the following adjectives: high, brilliant, sonorous, melodic, and so on.

A tone is a sound sensation that allows it to be classified as high or low. This value is also subjective and cannot be measured by any instrument. The tone is associated with an objective value - the frequency of the sound wave, but there is no unambiguous connection between them. For example, for a single frequency sound of constant intensity, the tone increases with increasing frequency. If the frequency of the sound remains constant, and its intensity increases, then the tone becomes lower.

Sound source shape

In accordance with the shape of the body, which performs mechanical vibrations and thus generates waves, there are three main types:

1. Point source. It creates spherical sound waves that decay rapidly with distance from the source (approximately 6 dB if the distance from the source is doubled).
2. Linear source. It creates cylindrical waves whose intensity decays more slowly than from a point source (for every doubling of the distance from the source, the intensity decreases by 3 dB).
3. Flat or two-dimensional source. It only generates waves in a specific direction. An example of such a source would be a piston moving in a cylinder.

Electronic sound sources

To create a sound wave, electronic sources use a special membrane (speaker), which makes mechanical vibrations due to the phenomenon of electromagnetic induction. These sources include the following:

• players of various discs (CD, DVD and others);
• cassette tape recorders;
• radio receivers;
• tVs and some others.

1. Sound. Basic characteristics of the sound field. Sound propagation

AND. Sound wave parameters

Sound vibrations of particles of an elastic medium are complex and can be represented as a function of time a \u003d a (t) (Figure 3.1, and).

Fig. 3.

1 ... Vibrations of air particles.

The simplest process is described by a sinusoid (Fig. 3.

1, b)

,

where a max - vibration amplitude;w \u003d 2 p f - angular frequency; f - vibration frequency.

Harmonic vibrations with amplitude a max and frequency f are called tone.

Complex fluctuations are characterized by the effective value on the time period T

For a sinusoidal process, the following relation is valid

For curves of a different shape, the ratio of the effective value to the maximum value is from 0 to 1.

Depending on the method of excitation of oscillations, there are:

· plane sound wave created by a flat vibrating surface;

· cylindrical sound wave, created by the radially oscillating side surface of the cylinder;

· spherical sound wave , created by a point source of oscillations such as a pulsating ball.

The main parameters characterizing the sound wave are:

· sound pressure p zv, Pa;

· sound intensity I, W / m 2.

· sound wavelength l, m;

· wave propagation speed from, m / s;

· vibration frequency f, Hz.

If oscillations are excited in a continuous medium, then they diverge in all directions. A good example is the vibrations of water waves. In this case, the speed of propagation of mechanical vibrations should be distinguished u (in our case, the visible transverse vibrations of water) and speed of propagation of disturbing action from(longitudinal acoustic vibrations).

From a physical point of view, the propagation of vibrations consists in the transfer of a momentum of motion from one molecule to another. Due to elastic intermolecular bonds, the movement of each of them repeats the movement of the previous one. The transfer of momentum requires a certain amount of time, as a result of which the movement of molecules at the observation points occurs with a delay in relation to the movement of molecules in the zone of excitation of oscillations. Thus, vibrations propagate at a certain speed. Sound wave propagation speed fromis a physical property of the environment.

Wavelength l is equal to the length of the path traversed by the sound wave in one period T:

where from - sound speed , T \u003d1/ f.

Sound vibrations in the air lead to its compression and rarefaction. In areas of compression, the air pressure increases, and in areas of rarefaction, it decreases.The difference between the pressure existing in the disturbed environment p Wed at the moment, and atmospheric pressure p atm, called sound pressure (Figure 3.3). In acoustics, this parameter is the main one through which all the others are determined.

p star \u003d p Wed - p atm. (3.1)

Figure 3.3. Sound pressure

The environment in which the sound propagates has specific acoustic impedance z A, which is measured in Pa* s / m (or in kg / (m 2 * c) and is the ratio of sound pressure p sv to the vibrational velocity of the particles of the medium u

z A \u003d p star / u \u003d r * s, (3.2)

where from - sound speed , m;r - density of the medium, kg / m 3.

For different mean values z A are different.

A sound wave is a carrier of energy in the direction of its movement. The amount of energy transferred by a sound wave in one second through a section of 1 m 2 perpendicular to the direction of motion is called sound intensity . Sound intensity is determined by the ratio of sound pressure to acoustic impedance of the medium W / m 2:

For a spherical wave from a sound source with a power W, W sound intensity on the surface of a sphere of radius requals

I= W / (4 pr 2),

that is the intensity spherical wave decreases with increasing distance from the sound source. When plane wave sound intensity is independent of distance.

Objective

To study the basics of the theory of sound recording and reproduction, the main characteristics of sound, methods of transforming sound, the device and features of the use of equipment for converting and amplifying sound, to acquire skills in their practical application.

Theoretical background

By sound is called the oscillatory motion of particles of an elastic medium, propagating in the form of waves in a gaseous, liquid or solid medium, which, acting on the human auditory analyzer, cause auditory sensations. The source of sound is an oscillating body, for example: vibrations of a string, vibration of a tuning fork, movement of a speaker cone, etc.

Sound wave the process of directed propagation of vibrations of an elastic medium from a sound source is called. The area of \u200b\u200bspace in which a sound wave propagates is called a sound field. A sound wave is an alternation of compressions and discharges of air. In the area of \u200b\u200bcompression, the air pressure exceeds atmospheric, in the area of \u200b\u200bvacuum - less than it. The variable part of atmospheric pressure is called sound pressure R ... Sound pressure unit - Pascal ( Pa) (Pa \u003d N / m 2)... Oscillations that have a sinusoidal shape (Fig. 1) are called harmonic. If a body emitting sound vibrates according to a sinusoidal law, then the sound pressure also changes according to a sinusoidal law. It is known that any complex vibration can be represented as the sum of simple harmonic vibrations. The sets of values \u200b\u200bof the amplitudes and frequencies of these harmonic oscillations are called respectively amplitude spectrum and frequency spectrum.

The oscillatory motion of air particles in a sound wave is characterized by a number of parameters:

Oscillation period(T), the smallest time interval after which the values \u200b\u200bof all physical quantities characterizing the oscillatory motion are repeated, during this time one complete oscillation is performed. The oscillation period is measured in seconds ( from).

Oscillation frequency (f) , the number of complete oscillations per unit of time.

where: f - vibration frequency; T - period of fluctuations.

The frequency unit is hertz ( Hz) - one full oscillation per second (1 kHz = 1000 Hz).

Figure: 1. Simple harmonic oscillation:
A is the amplitude of the oscillation, T is the period of the oscillation

Wavelength (λ ), the distance at which one oscillation period fits. Wavelength is measured in meters ( m). The wavelength and frequency of vibration are related by the relationship:

where from Is the speed of sound propagation.

Vibration amplitude (AND) , the greatest deviation of the fluctuating value from the state of rest.

Oscillation phase.

Imagine a circle whose length is equal to the distance between points A and Ε (Fig. 2), or the wavelength at a certain frequency. As this circle "rotates", its radial line in each individual place of the sinusoid will be at a certain angular distance from the starting point, which will be the phase value at each such point. The phase is measured in degrees.

When a sound wave collides with a surface, it is partially reflected at the same angle at which it hits this surface, while its phase does not change. In fig. 3 illustrates the phase dependence of reflected waves.

Figure: 2. Sine wave: amplitude and phase.
If the circumference is equal to the wavelength at a certain frequency (distance from A to E), then as it rotates, the radial line of this circle will show the angle corresponding to the phase value of the sinusoid at a particular point

Figure: 3. Phase dependence of reflected waves.
Sound waves of different frequencies emitted by a sound source with the same phase, after passing the same distance, reach a surface with a different phase

A sound wave is capable of bending around obstacles if its length is greater than the dimensions of the obstacle. This phenomenon is called diffraction... Diffraction is especially noticeable at low frequency vibrations with a significant wavelength.

If two sound waves have the same frequency, then they interact with each other. The interaction process is called interference. With the interaction of in-phase (in phase) oscillations, the sound wave is amplified. In the case of interaction of antiphase oscillations, the resulting sound wave weakens (Fig. 4). Sound waves, the frequencies of which differ significantly from each other, do not interact with each other.

Figure: 4. Interaction of oscillations in phase (a) and in antiphase (b):
1, 2 - interacting vibrations, 3 - resulting vibrations

Sound vibrations can be damped and non-damped. The amplitude of the damped oscillations gradually decreases. An example of damped vibrations is the sound that occurs when a string is struck once or a gong is struck. The reason for the damping of string vibrations is the friction of the string against the air, as well as friction between the particles of the vibrating string. Continuous oscillations can exist if frictional losses are compensated by an influx of energy from the outside. An example of sustained vibrations is school bell vibrations. As long as the power button is pressed, there are undamped vibrations in the call. After stopping the supply of energy to the bell, the oscillations damp.

Spreading from its source in the room, the sound wave carries energy, expands until it reaches the boundary surfaces of this room: walls, floor, ceiling, etc. The propagation of sound waves is accompanied by a decrease in their intensity. This is due to the loss of sound energy to overcome friction between air particles. In addition, propagating in all directions from the source, the wave covers an ever larger area of \u200b\u200bspace, which leads to a decrease in the amount of sound energy per unit area, with each doubling of the distance from the spherical source, the vibration force of air particles decreases by 6 dB (four times in power) (fig. 5).

Figure: 5. The energy of a spherical sound wave is distributed over an increasing area of \u200b\u200bthe wavefront, due to which the sound pressure loses 6 dB with each doubling of the distance from the source

Meeting an obstacle on its way, part of the energy of a sound wave passes through the walls, part absorbed inside the walls, and part reflected back inside the room. The energy of the reflected and absorbed sound wave is equal to the energy of the incident sound wave. To varying degrees, all three types of sound energy distribution are present in almost all cases.
(fig. 6).

Figure: 6. Reflection and absorption of sound energy

The reflected sound wave, having lost some of the energy, will change direction and will propagate until it reaches other surfaces of the room, from which it will be reflected again, while losing some more energy, etc. This will continue until the energy of the sound wave is finally extinguished.

The reflection of a sound wave occurs according to the laws of geometric optics. High density substances (concrete, metal, etc.) reflect sound well. There are several reasons for the absorption of a sound wave. A sound wave spends its energy on vibrations of the obstacle itself and on air vibrations in the pores of the surface layer of the obstacle. It follows that porous materials (felt, foam rubber, etc.) strongly absorb sound. A room filled with spectators has more sound absorption than an empty one. The degree of reflection and absorption of sound by a substance is characterized by the coefficients of reflection and absorption. These factors can range from zero to one. A factor of one indicates perfect reflection or absorption of sound.

If the sound source is in the room, then the listener receives not only direct, but also sound energy reflected from various surfaces. The sound volume in a room depends on the power of the sound source and the amount of sound absorbing material. The more sound-absorbing material is placed in the room, the lower the sound volume.

After the sound source is turned off due to the reflections of sound energy from various surfaces, a sound field exists for some time. The process of gradual attenuation of sound in closed rooms after turning off its source is called reverb. The duration of the reverberation is characterized by the so-called. reverberation time, i.e. the time during which the sound intensity decreases by 10 6 times, and its level by 60 dB . For example, if the sound of an orchestra in a concert hall reaches 100 dB with a background noise level of about 40 dB, then the final chords of the orchestra, when decaying, will dissolve into noise when their level drops by about 60 dB. Reverberation time is the most important factor in determining the acoustic quality of a room. The larger the volume of the room and the lower the absorption on the limiting surfaces, the larger it is.

The amount of reverberation time affects the intelligibility of speech and the sound quality of the music. If the reverberation time is too long, speech becomes illegible. If the reverberation time is too short, speech is intelligible, but the sound of the music becomes unnatural. The optimal reverberation time, depending on the volume of the room, is about 1–2 s.

Basic characteristics of sound.

Sound speed in the air is equal to 332.5 m / s at 0 ° С. At room temperature (20 ° C) the speed of sound is about 340 m / s. The speed of sound is indicated by the symbol “ from ».

Frequency.The sounds perceived by the human auditory analyzer form a range of sound frequencies. It is generally accepted that this range is limited to frequencies from 16 to 20,000 Hz. These boundaries are very arbitrary, which is associated with the individual characteristics of people's hearing, age-related changes in the sensitivity of the auditory analyzer and the method of recording auditory sensations. A person can distinguish a frequency change of 0.3% at a frequency of the order of 1 kHz.

The physical concept of sound encompasses both audible and inaudible vibration frequencies. Sound waves with a frequency below 16 Hz are conventionally called infrasound, above 20 kHz - ultrasound . The region of infrasonic frequencies from below is practically unlimited - in nature there are infrasonic vibrations with a frequency of tenths and hundredths of a Hz .

The sound range is conventionally divided into several narrower ranges (Table 1).

Table 1

The range of audio frequencies is conventionally divided into sub-bands

Sound intensity(W / m2) is determined by the amount of energy carried by the wave per unit of time through a unit of surface area perpendicular to the direction of wave propagation. The human ear perceives sound in a very wide range of intensity: from the faintest audible sounds to the loudest, for example, created by the engine of a jet plane.

The minimum sound intensity at which an auditory sensation occurs is called the auditory threshold. It depends on the frequency of the sound (Fig. 7). The human ear has the highest sensitivity to sound in the frequency range from 1 to 5 kHz, respectively, and the threshold of auditory perception here has the lowest value of 10 -12 W / m 2. This value is taken as zero audibility level. Under the action of noises and other sound stimuli, the audibility threshold for a given sound rises (Sound masking is a physiological phenomenon, which consists in the fact that when two or more sounds of different loudness are perceived simultaneously, quieter sounds cease to be audible), and the increased value persists for some time after termination of the interfering factor, and then gradually returns to its original level. In different people and in the same persons at different times, the hearing threshold may differ depending on age, physiological state, fitness.

Figure: 7. Frequency dependence of the standard hearing threshold
sinusoidal signal

Sounds of high intensity cause a pressing pain in the ears. The minimum sound intensity at which there is a feeling of pressing pain in the ears (~ 10 W / m 2) is called the pain threshold. Just like the auditory threshold, the pain threshold depends on the frequency of sound vibrations. Sounds that approach the pain threshold are harmful to hearing.

Normal sound sensation is possible if the sound intensity is between the threshold of hearing and the threshold of pain.

It is convenient to evaluate the sound by the level ( L) intensity (sound pressure), calculated by the formula:

where J 0 - auditory threshold, J -sound intensity (Table 2).

table 2

Characterization of sound by intensity and its assessment by the level of intensity relative to the threshold of auditory perception

Sound characteristic	Intensity (W / m2)	Intensity level relative to auditory threshold (dB)
Hearing threshold	10 -12
Heart sounds generated through a stethoscope	10 -11
Whisper	10 -10 –10 -9	20–30
Speech sounds during quiet conversation	10 -7 –10 -6	50–60
Noise associated with heavy traffic	10 -5 –10 -4	70–80
The noise generated by a rock concert	10 -3 –10 -2	90–100
Noise near a running aircraft engine	0,1–1,0	110–120
Pain threshold

Our hearing aids are capable of capturing a huge dynamic range. Changes in air pressure caused by the quietest audible sounds are in the order of 2 × 10 -5 Pa. At the same time, the sound pressure, with a level approaching the pain threshold for our ears, is about 20 Pa. As a result, the ratio between the quietest and loudest sounds that our hearing aids can perceive is 1: 1,000,000. It is rather inconvenient to measure such signals of different level on a linear scale.

In order to compress such a wide dynamic range, the concept of "bel" was introduced. Bel is the simple logarithm of the ratio of two degrees; a decibel is equal to one tenth of a bel.

To express acoustic pressure in decibels, you need to square the pressure (in Pascals) and divide it by the square of the reference pressure. For convenience, the squaring of the two pressures is performed outside the logarithm (which is a property of logarithms).

To convert acoustic pressure to decibels, the formula is applied:

where: P is the acoustic pressure of interest to us; P 0 - initial pressure.

When 2 × 10 -5 Pa is taken as the reference pressure, the sound pressure, expressed in decibels, is called the sound pressure level (SPL - from the English sound pressure level). Thus, a sound pressure equal to 3 Pa, is equivalent to a sound pressure level of 103.5 dB, therefore:

The above-mentioned acoustic dynamic range can be expressed in decibels as the following sound pressure levels: from 0 dB for the quietest sounds, 120 dB for sounds at the pain threshold level, up to 180 dB for the loudest sounds. At 140 dB, severe pain is felt, at 150 dB, ear damage occurs.

Sound volume, a quantity characterizing the auditory sensation for a given sound. The sound volume is complexly dependent on sound pressure (or sound intensity), frequencies and modes of vibrations. At a constant frequency and form of vibrations, the sound volume increases with increasing sound pressure (Fig. 8.). The loudness of the sound of a given frequency is estimated by comparing it with the loudness of a simple tone with a frequency of 1000 Hz. The sound pressure level (in dB) of a pure tone with a frequency of 1000 Hz, as loud (by comparison by ear) as the sound being measured, is called the loudness level of this sound (in backdrops) (fig. 8).

Figure: 8. Curves of equal loudness - the dependence of the sound pressure level (in dB) on the frequency at a given loudness (in backgrounds).

Sound spectrum.

The nature of the perception of sound by the organs of hearing depends on its frequency spectrum.

Noise has a continuous spectrum, i.e. the frequencies of the simple sinusoidal oscillations contained in them form a continuous series of values \u200b\u200bthat completely fill a certain interval.

Musical (tonal) sounds have a linear frequency spectrum. The frequencies of the simple harmonic oscillations included in them form a number of discrete values.

Each harmonic vibration is called a tone (simple tone). The pitch depends on the frequency: the higher the frequency, the higher the pitch. The perceived pitch of a sound is determined by its frequency. A smooth change in the frequency of sound vibrations from 16 to 20,000 Hz is perceived at first as a low-frequency hum, then as a whistle, gradually turning into a squeak.

The fundamental tone of a complex musical sound is the tone corresponding to the lowest frequency in its spectrum. Tones corresponding to the rest of the spectrum are called overtones. If the frequencies of the overtones are multiples of the frequency f о of the fundamental tone, then the overtones are called harmonic, and the fundamental tone with the frequency f о is called the first harmonic, the overtone with the next highest frequency 2f о - the second harmonic, etc.

Musical sounds with the same pitch may differ in timbre. Timbre is determined by the composition of overtones - their frequencies and amplitudes, as well as the nature of the rise in amplitudes at the beginning of the sound and their decay at the end of the sound.

Similar information.

2.2 Sound waves and their properties

Sound is mechanical vibrations that propagate in an elastic medium: air, water, solid, etc.

A person's ability to perceive elastic vibrations, to listen to them is reflected in the name of the doctrine of sound - acoustics.

In general, the human ear hears sound only when mechanical vibrations with a frequency of at least 16 Hz but not higher than 20,000 Hz act on the hearing aid of the ear. Vibrations with lower or higher frequencies are inaudible to the human ear.

That air is a conductor of sound was proven by the experience of Robert Boyle in 1660. If a sounding body, for example an electric bell, is placed under the bell of an air pump, then as the air is pumped out from under it, the sound will become weaker and finally stop.

During its vibrations, the body alternately compresses the air layer adjacent to its surface, then, on the contrary, creates a rarefaction in this layer. Thus, the propagation of sound in air begins with fluctuations in the density of air at the surface of an oscillating body.

The process of propagation of vibrations in space over time is called a wave. The wavelength is the distance between the two nearest particles of the medium, which are in the same state.

The physical quantity equal to the ratio of the wavelength to the oscillation period of its particles is called the wave speed.

Oscillations of the particles of the medium in which the wave propagates are forced. Therefore, their period is equal to the period of oscillations of the wave exciter. However, the speed of propagation of waves in different media is different.

Sounds are different. We easily distinguish between the whistle and the beat of the drum, the male voice (bass) from the female (soprano).

Some sounds are said to be low-pitched, others we call high-pitched sounds. The ear can easily distinguish them. The sound produced by the big drum is a low-pitched sound, the whistle is a high-pitched sound.

Simple measurements (vibration sweep) show that low-tone sounds are low-frequency vibrations in a sound wave. A high-pitched sound corresponds to a high vibration frequency. The frequency of vibration in a sound wave determines the tone of the sound.

There are special sound sources that emit a single frequency, the so-called pure tone. These are tuning forks of various sizes - simple devices in the form of curved metal rods with legs. The larger the tuning fork, the lower the sound it emits when struck.

If you take several tuning forks of different sizes, it will not be difficult to arrange them by ear in ascending order of pitch. Thus, they will be located in size: the largest tuning fork gives a low sound, and the smallest one - the highest.

Even sounds of the same tone can be of different volumes. The loudness of a sound is related to the vibration energy in the source and in the wave. The vibration energy is determined by the vibration amplitude. Loudness therefore depends on the amplitude of the vibration.

The fact that the propagation of sound waves does not occur instantaneously can be seen from the simplest observations. If in the distance there is a thunderstorm, a shot, an explosion, a steam locomotive whistle, an ax blow, etc., then at first all these phenomena are visible, and only then, after a while, a sound is heard.

Like any wave, a sound wave is characterized by the speed of propagation of oscillations in it.

The speed of sound is different in different environments. For example, in hydrogen, the propagation speed of sound waves of any length is 1284 m / s, in rubber - 1800 m / s, and in iron - 5850 m / s.

Now acoustics, as a field of physics, considers a wider range of elastic vibrations - from the lowest to the highest, up to 1012 - 1013 Hz. Sound waves inaudible to humans with frequencies below 16 Hz are called infrasound, sound waves with frequencies from 20,000 Hz to 109 Hz are called ultrasound, and vibrations with frequencies higher than 109 Hz are called hypersound.

There are many uses for these inaudible sounds.

Ultrasounds and infrasounds have a very important role in the living world. For example, fish and other marine animals are sensitive to the infrasonic waves generated by storm surges. Thus, they sense the approach of a storm or cyclone in advance, and swim away to a safer place. Infrasound is a component of the sounds of the forest, sea, atmosphere.

When the fish moves, elastic infrasonic vibrations are created that propagate in the water. These vibrations are well felt by sharks for many kilometers and swim towards prey.

Ultrasounds can be emitted and perceived by animals such as dogs, cats, dolphins, ants, bats, etc. Bats emit short, high-pitched sounds during flight. In their flight, they are guided by the reflections of these sounds from objects encountered on the way; they can even catch insects, guided only by the echoes from their small prey. Cats and dogs can hear very high-pitched whistling sounds (ultrasounds).

Echo is a wave reflected from an obstacle and received by the observer. Sound echo is perceived by the ear separately from the primary signal. The echo phenomenon is based on the method of determining the distances to various objects and detecting their locations. Let us assume that a sound signal is emitted by some sound source and the moment of its emission is fixed. The sound met some kind of obstacle, bounced off it, returned and was received by the sound receiver. If the time interval between the moments of emission and reception was measured, then it is easy to find the distance to the obstacle. In the measured time t, the sound traveled the distance 2s, where s is the distance to the obstacle, and 2s is the distance from the sound source to the obstacle and from the obstacle to the sound receiver.

This formula can be used to find the distance to the signal reflector. But you also need to know where he is, in which direction from the source the signal met him. Meanwhile, the sound propagates in all directions, and the reflected signal could come from different directions. To avoid this difficulty, not ordinary sound is used, but ultrasound.

The main feature of ultrasonic waves is that they can be made directional, propagating in a certain direction from the source. Thanks to this, by the reflection of ultrasound, you can not only find the distance, but also find out where the object that reflected them is located. This can, for example, measure the depth of the sea under a ship.

Sound radars allow detecting and locating various damages in products, for example, voids, cracks, foreign inclusions, etc. In medicine, ultrasound is used to detect various anomalies in the patient's body - tumors, distortions of the shape of organs or parts thereof, etc. The shorter the ultrasonic wavelength, the smaller the size of the detected parts. Ultrasound is also used to treat certain diseases.

Ocean Acoustics

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Study of sound waves

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The singing of birds, the sound of rain and wind, the rolling of thunder, music - everything that we hear we consider to be sound.

Scientifically speaking, sound is a physical phenomenon that is mechanical vibrations propagating in solid, liquid and gaseous media... They also cause auditory sensations.

How the sound wave appears

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All sounds propagate in the form of elastic waves. And waves arise under the influence of elastic forces that appear when the body is deformed. These forces seek to return the body to its original state. For example, a stretched string does not sound when stationary. But one has only to take it aside, as under the influence of the force of elasticity, it will tend to take its original position. By vibrating, it becomes a sound source.

The sound source can be any oscillating body, for example, a thin steel plate fixed on one side, air in a musical wind instrument, human vocal cords, a bell, etc.

What happens in the air when wobble occurs?

Like any gas, air is elastic. It resists compression and immediately begins to expand when the pressure decreases. Any pressure on him, he evenly transfers in different directions.

If the air is compressed sharply with the help of the piston, then the pressure will immediately increase in this place. It will immediately be transferred to neighboring air layers. They will shrink and the pressure in them will increase, and in the previous layer will decrease. So along the chain, alternating zones of high and low pressure are transmitted further.

Bending to the sides alternately, the sounding string compresses the air, first in one direction, and then in the opposite direction. In the direction where the string deviated, the pressure becomes higher than atmospheric by some value. On the opposite side, the pressure decreases by the same amount, since the air is rarefied there. Compression and rarefaction will alternate and spread in different directions, causing the air to vibrate. These vibrations are called sound wave ... And the difference between atmospheric pressure and pressure in the layer of compression or rarefaction of air is called acoustic, or sound pressure.

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A sound wave propagates not only in air, but also in liquid and solid media. For example, water perfectly conducts sound. We hear a stone strike underwater. The noise of the surface ship's propellers is picked up by the submarine's acoustics. If we put a mechanical watch on one end of a wooden board, then, putting our ear to the opposite end of the board, we will hear its ticking.

Will sounds be different in a vacuum? English physicist, chemist and theologian Robert Boyle, who lived in the 17th century, placed the clock in a glass vessel from which he evacuated air. He did not hear the tick of the clock. This meant that sound waves did not propagate in airless space.

Sound wave characteristics

The form of sound vibrations depends on the sound source. Uniform or harmonic oscillations have the simplest form. They can be represented as a sinusoid. Such oscillations are characterized by amplitude, wavelength and frequency of propagation of oscillations.

Amplitude

Amplitude in the general case, the maximum deviation of the body from the equilibrium position is called.

Since a sound wave consists of alternating areas of high and low pressure, it is often considered as a process of propagation of pressure fluctuations. Therefore, they talk about air pressure amplitude in the wave.

The volume of the sound depends on the amplitude. The larger it is, the louder the sound.

Each sound of human speech has a vibration form that is unique to it. So, the form of vibration of sound "a" differs from the form of vibration of sound "b"

Wave frequency and period

The number of vibrations per second is called wave frequency .

f \u003d 1 / T

where T - period of fluctuations. This is a period of time during which one complete oscillation is performed.

The longer the period, the lower the frequency, and vice versa.

The unit of measurement for frequency in the international SI system is hertz (Hz). 1 Hz is one vibration per second.

1 Hz \u003d 1 s -1.

For example, a frequency of 10 Hz means 10 vibrations per second.

1,000 Hz \u003d 1 kHz

The pitch depends on the vibration frequency. The higher the frequency, the higher the pitch of the sound.

The human ear is not able to perceive all sound waves, but only those that have a frequency of 16 to 20,000 Hz. It is these waves that are considered sound. Waves with a frequency below 16 Hz are called infrasonic, and above 20,000 Hz are called ultrasonic.

A person does not perceive either infrasonic or ultrasonic waves. But animals and birds are capable of hearing ultrasound. For example, the common butterfly distinguishes sounds with a frequency of 8,000 to 160,000 Hz. The range perceived by dolphins is even wider, it ranges from 40 to 200 thousand Hz.

Wavelength

Wavelength is the distance between two nearest points of a harmonic wave that are in the same phase, for example, between two crests. Denoted as ƛ .

For a time equal to one period, the wave travels a distance equal to its length.

Wave propagation speed

v = ƛ / T

Because T \u003d 1 / f,

then v \u003d ƛ f

Sound speed

Attempts to determine the speed of sound using experiments were made as early as the first half of the 17th century. The English philosopher Francis Bacon in his work "New Organon" proposed his own way of solving this problem, based on the difference in the speeds of light and sound.

It is known that the speed of light is much higher than the speed of sound. Therefore, during a thunderstorm, first we see a flash of lightning, and only then we hear thunderclaps. Knowing the distance between the light and sound source and the observer, as well as the time between the flash of light and sound, the speed of sound can be calculated.

French scientist Maren Marsenne took advantage of Bacon's idea. An observer at some distance from the man firing the musket recorded the time elapsed from the flash of light to the sound of the shot. Then the distance was divided by time and the speed of sound was obtained. According to the results of the experiment, the speed turned out to be 448 m / s. This was a rough estimate.

At the beginning of the 19th century, a group of scientists from the Paris Academy of Sciences repeated this experience. According to their calculations, the speed of light was 350-390 m / s. But this figure was not accurate either.

Theoretically, Newton tried to calculate the speed of light. He based his calculations on the Boyle-Mariotte law, which described the behavior of gas in isothermal process (at constant temperature). And this happens when the volume of gas changes very slowly, having time to give the environment the heat that arises in it.

Newton, on the other hand, assumed that between the regions of compression and rarefaction, the temperature levels out quickly. But these conditions are not present in the sound wave. Air does not conduct heat well, and the distance between the compression and rarefaction layers is large. The heat from the compression layer does not have time to transfer to the rarefaction layer. And between them there is a temperature difference. Therefore, Newton's calculations turned out to be wrong. They gave a figure of 280 m / s.

The French scientist Laplace was able to explain that Newton's mistake was that a sound wave propagates in air in adiabatic conditions at varying temperatures. According to Laplace's calculations, the speed of sound in air at a temperature of 0 ° C is 331.5 m / s. Moreover, it increases with increasing temperature. And when the temperature rises to 20 ° C, it will already be equal to 344 m / s.

Sound waves travel at different speeds in different environments.

For gases and liquids, the speed of sound is calculated by the formula:

where from -sound speed,

β - adiabatic compressibility of the medium,

ρ - density.

As can be seen from the formula, the speed depends on the density and compressibility of the medium. It is less in air than in liquid. For example, in water at a temperature of 20 ° C, it is equal to 1484 m / s. Moreover, the higher the salinity of the water, the faster the sound propagates in it.

For the first time the speed of sound in water was measured in 1827. This experiment was somewhat reminiscent of the measurement of the speed of light by Maren Marsen. A bell was lowered from one boat into the water. At a distance of more than 13 km from the first boat was the second. On the first boat, the bell was struck while gunpowder was set on fire. On the second boat, the flash time was recorded, and then the time of arrival of the sound from the bell. By dividing the distance by time, we obtained the speed of a sound wave in water.

Sound has the highest speed in a solid environment. For example, in steel it reaches more than 5000 m / s.