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Reflection of a sound wave from clouds. Reflection of sound from obstacles and at the boundary of two media

Sound spreads from a sounding body evenly in all directions if there are no obstacles in its path. But not every obstacle can limit its spread. You cannot shield yourself from sound with a small sheet of cardboard, as you can from a beam of light. Sound waves, like any waves, are capable of bending around obstacles and “not noticing” them if their dimensions are smaller than the wavelength. The length of sound waves audible in the air ranges from 15 m to 0.015 m. If the obstacles in their path are smaller (for example, tree trunks in a light forest), then the waves simply bend around them. A large obstacle (a wall of a house, a rock) reflects sound waves according to the same law as light waves: the angle of incidence is equal to the angle of reflection. Echo is the reflection of sound from obstacles.

Sound moves from one environment to another in a unique way. This phenomenon is quite complex, but it obeys general rule: sound does not pass from one medium to another if their densities are sharply different, for example, from water to air. Reaching the boundaries of these environments, it is almost completely reflected. A very small part of its energy is spent on vibration surface layers another environment. Having immersed your head under the very surface of the river, you will still hear loud sounds, but at a depth of 1 m you will no longer hear anything. Fish do not hear the sound heard above the surface of the sea, but they hear the sound from a body vibrating in the water well.

Sound is heard through thin walls because it causes them to vibrate, and they seem to reproduce the sound in another room. Good soundproofing materials - cotton wool, fleecy carpets, walls made of foam concrete or porous dry plaster - are precisely different in that they have a lot of interfaces between air and a solid body. Passing through each of these surfaces, sound is reflected many times. But, in addition, the very medium in which sound propagates absorbs it. The same sound is heard better and further in clean air than in fog, where it is absorbed by the interface between air and water droplets.

Sound waves of different frequencies are absorbed differently in the air. Stronger - high-pitched sounds, less - low-pitched sounds, such as bass. This is why a steamship whistle makes such a low sound (its frequency is no more than 50 Hz): a low sound is heard at a greater distance. Big bell in the Moscow Kremlin, when it was still hanging on the Ivan the Great bell tower, it was heard 30 miles away - it hummed in a tone of approximately 30 Hz (f suboctave). Infrasounds are absorbed even less, especially in water. Fish hear them tens and hundreds of kilometers away. But ultrasound is absorbed very quickly: ultrasound with a frequency of 1 MHz is attenuated in air by half at a distance of 2 cm, while sound at 10 kHz is attenuated by half at 2200 m.

Sound wave energy

The chaotic movement of particles of matter (including air molecules) is called thermal. When a sound wave propagates in the air, its particles acquire, in addition to thermal, an additional movement - oscillatory. The energy for such movement is given to air particles by a vibrating body (sound source); While it oscillates, energy is continuously transferred from it to the surrounding air. The further a sound wave travels, the weaker it becomes, the less energy it contains. The same thing happens with a sound wave in any other elastic medium - in a liquid, in a metal.

The sound spreads evenly in all directions, and at each moment the layers of compressed air, arising from one impulse, form, as it were, the surface of a ball, in the center of which there is a sounding body. The radius and surface of such a “ball” are constantly growing. The same amount of energy falls on a larger and larger surface of the “ball”. The surface of the ball is proportional to the square of the radius, therefore the amount of energy of a sound wave passing, say, through a square meter of surface is inversely proportional to the square of the distance from the sounding body. Consequently, the sound becomes weaker with distance. Russian scientist N.A. Umov introduced into science the concept of energy density flow. The magnitude of the energy flow is convenient for measuring the strength (intensity) of sound. The energy density flux in a sound wave is the amount of energy that passes per second through a unit surface perpendicular to the direction of the wave. The greater the energy density flow, the greater the sound intensity. Energy flow is measured in watts per square meter (W/m²).

Propagation of sound in free space

If the sound source omnidirectional, in other words, sound energy spreads evenly in all directions, such as the sound from an airplane in the air, then the sound pressure distribution depends only on distance and decreases by 6 dB with each doubling of the distance from the sound source.

If the sound source directed, such as a horn, then the sound pressure level depends on both the distance and the angle of perception relative to the axis of sound emission.

Interaction of sound with an obstacle

Sound (audible) waves, encountering an obstacle on their way, are partially absorbed by it, partially reflected from it, that is, they are re-emitted by the obstacle back into the room and partially pass through it.

It should immediately be noted that the percentage of these processes will be different for sound waves of different lengths, which is due to the peculiarities of the behavior of HF, MF and LF waves. In addition, an important role is played by the characteristics of the obstacle itself, such as its thickness, the density of the material from which it is made, as well as the properties of the surface (smooth/embossed, dense/loose).

Propagation of sound in a confined space

The propagation of sound in a confined space (indoor conditions) is fundamentally different from the conditions for its propagation in free space, since the sound wave encounters many obstacles on its path (walls, ceiling, floor, furniture, interior items, etc.).

The resulting numerous reflections of the main sound interact both with the direct sound emanating directly from the speaker and reaching the listener’s ears in the shortest way, that is, in a straight line, and with each other. The following diagram illustrates this difference schematically:

1) Open space: direct sound;

2) Closed space: direct sound + early reflections + reverberation.

Everyone knows that sound reflects off walls, floors and ceilings, but how does this happen?

As already discussed above, a sound wave, hitting an obstacle, is partially reflected from it, partially absorbed, and partially passes through the obstacle.

Naturally, the harder and denser the wall, the more of the acoustic energy it will reflect back into the interior of the room.

Sound waves are reflected from obstacles in a highly directional manner, therefore, in places where they are reflected from walls, ceilings and floors, that is, away from the main sound source, they appear. additional "images"(secondary, “imaginary” sound sources or so-called “phantoms”. In some foreign sources of information they are also called “hot areas”).

Reflections, interacting with each other and with direct sound, distort it and worsen the clarity of the sound picture. Now imagine what happens when multi-frequency sound from two or more acoustic systems is reflected from six surfaces of the room at once (four walls, ceiling and floor), and you will understand what a colossal influence the acoustics of the room has on the quality of the sound reproduced in it .

So, in a confined space (indoor conditions) there are three sound sources:

1. Direct sound- this is the sound that comes directly from the speakers of the speaker system (acoustic system) and reaches the listener’s ears in the shortest way - in a straight line, that is, without being reflected from the surfaces of the walls, floor and ceiling of the room (it can be conditionally considered as the original sound recorded on a musical medium).

2. Early reflections (first reflections)- these are reflections of the main sound from the walls, floor and ceiling of the room, as well as from the interior objects located in it, reaching the listener’s ears in the shortest ways, that is, undergoing one single reflection, due to which they retain a sufficiently large amplitude and form in the areas of reflection on the surfaces of walls, floors and ceilings of the room "images"(secondary, virtual, “imaginary” sources, “phantoms”) of direct sound. That is why the first reflections are the most important in the overall structure of reflections and, accordingly, have a serious impact on the sound quality and the formation of a stereo image.

3. Reverberation reflections (late reflections, reverberation, echo). Unlike early reflections, they are the result of multiple reflections of the main sound from the surfaces of the walls, floor and ceiling of the room. They reach the listener's ears via complex, long paths and therefore have low amplitude.

Under main sound refers to sound coming directly from the speaker, but, unlike direct sound, has a circular direction.

What is the difference between early and late reflections?

To answer this question, you need to familiarize yourself with some subjective features human sound perception associated with the temporal characteristics of sound.

This is the so-called Haas effect, the essence of which is that if a sound arrives from several sources at different distances, then our ear/brain system identifies (perceives) only the sound that came first.

If the difference in arrival time of several audio signals is up to 50 ms, then the earlier arriving sound dominates the later arriving sound, even if the latter is 10 dB louder (i.e. 3 times louder!!!).

Thus, all reflections that reach the listener’s ears during the first 50 ms following the direct sound are perceived by the human ear together with the direct signal, that is, as one common signal.

On the one hand, this leads to an improvement in the perception of speech and a subjective increase in its volume, however, in the case of sound reproduction, this significantly worsens its quality due to the distortion of the original musical information by reflected sound signals merging with it.

If the reflections arrive with a delay of more than 50 ms and have a comparable level to the direct signal, the human ear perceives them as a repetition of the direct signal, that is, in the form of separate sound signals. In such cases, these reflections are called "echo" (reverberation). Echo significantly impairs speech intelligibility and the perception of musical information.

1) Special practical significance have early reflections (first reflections), reaching the listener’s ear in a time interval of up to 20 ms. after a direct signal.

As already mentioned, they retain a large amplitude and are perceived by the human ear together with the direct signal and, therefore, distort its original structure. Thus, first reflections are one of the main enemies of high-quality sound.

The geometric characteristics of early reflections directly depend on the shape of the room, the location of the sound source (in our case, speakers) and the listener in it, being unique for each specific point in a given room.

The amplitude characteristics of the first reflections depend on:

Distances between the sound source and the reflecting surface;

Distances from the listener's ears to the reflective surface;

From the acoustic properties of the reflective surface itself.

Thus, the acoustic characteristic of each point in the interior space of a room is mainly determined by a combination of the characteristics of direct sound and early reflections arriving at that point.

2) Reverberation (late reflections, echo).

When playing sound in a room, we hear not only direct sound from the source and early reflections, but also weaker (quiet) reflected signals resulting from repeated long-term reflections of the main sound from the walls, floor and ceiling of the room. Naturally, these sound signals reach the listener's ears with a great delay relative to the moment of arrival of the direct sound and the first reflections. Subjectively, this is perceived in
the form of an echo.

Thus, the effect in which sound attenuation does not occur immediately, but gradually, due to its numerous reflections from the walls, floor and ceiling of the room, is called reverberation.

The spectral composition of reflected signals in large and small rooms is different, since reverberation carries information about the size of the room. In addition, the spectrum of reverberation signals also contains information about the properties of the materials from which the reflective surfaces are made.

For example, reverb with high level high-frequency components is associated with a room with solid walls that reflect high frequencies well. If the reverberation sound is dull, then the listener comes to the conclusion that the walls of the room are covered with carpets or draperies that absorb high frequencies.

It should also be noted that the spectrum of reverberation signals allows one to determine the distance to the sound source.

Our ear/brain system, automatically assessing the relationship between direct sound and reverberation levels, independently judges whether the sound source is close (weak reverberation) or far away (strong reverberation).

In addition, the human hearing organ is designed in such a way that the quality of sound perception depends not only on the quantitative relationship between direct sound and reverberation, but also on the delay time of the reverberation signal in relation to the moment of perception of direct sound.

Reverberation time represents a period of time during which a sound wave, repeatedly echoing around the room, gradually fades. This parameter is one of the main criteria acoustic characteristics premises.

This parameter characterizes the size of the room: in small rooms, a greater number of reflections occur per unit time, which, unlike the situation in large rooms, leads to a rapid weakening and subsequent attenuation of the reverberation. And also the properties of its reflective surfaces: hard glossy surfaces, unlike embossed and soft ones, reflect sound well, practically without weakening it, which in turn, naturally, prolongs the reverberation time.

To denote this parameter, the abbreviation was adopted RT60, that is, the time (in seconds) during which the sound pressure level (SPL) in a room decreases by 60 dB after the sound source stops emitting.

Multiple echoes are subjectively perceived as echo of the room. The lower the attenuation, the longer the reverberation time and, accordingly, the stronger the boom.

As already noted, reverberation time is determined not only by the size of the room, but also by the reflective ability of its walls, floor and ceiling. Have you ever noticed how unusual the sound is in an empty room prepared for renovation, or in a huge hangar where there is strong reverberation?

In connection with the above, it is advisable to consider another category, namely, boom radius. What it is?

We are talking about the relationship between the levels of direct and reflected sound. In general, the closer the listener is to the sound source, the louder the direct sound and, accordingly, the quieter the reflected sound. As you move away from the sound source, the direct sound weakens, and the reflected sound, on the contrary, intensifies.

Logically following this principle, we can quite rightly assume that at a certain distance from the sound source, direct and reflected sound will be perceived by the listener with the same loudness. So the circle, with a radius corresponding to the radius of the echo, is the boundary between two areas: the inner one, where direct sound predominates, and the outer one, where reflected sound dominates.

Features of the behavior of sound waves of different lengths in a confined space

It is obvious that the behavior of sound in a music studio is subject to the laws of its propagation in a confined space. Let's look at this process in more detail.

The behavior of sound waves in a confined space depends on their length and, accordingly, on the frequency of their vibrations, varying from 17 meters (20 Hz - at the beginning of the audible bass range) to 17 millimeters (20 KHz - at the end of the audible high-frequency range).

In a simplified way, the behavior of sound waves indoors, depending on their length, can be represented in the form of two independent models.

One - for LF it looks like a purely wave process - interference (addition) of all LF sources (both bass from speakers and low-frequency reflections from walls, floor and ceiling), leading to the formation of a three-dimensional picture for each frequency, like a mountainous terrain with alternating peaks and volume dips.

The second is for HF, similar to the emission of light with the known laws of refraction, reflection and diffraction. She uses visual methods geometric optics, since similar rules apply in these areas. For example, part of the energy of a sound wave that reaches a solid surface is reflected by it at an angle equal to the angle of incidence.

The general picture is complemented by the mixing of these two processes for the midrange.

Medium and high frequency waves (short wavelengths).

As already mentioned, the behavior of HF sound waves in general outline obeys the laws of light propagation. This directly applies to HF waves and is more or less true in relation to the VHF subband.

The first feature of sound waves in this range is their pronounced focus, that is, a change (increase or weakening) in the perception of the HF level even with a slight deviation from the axis of their radiation. Simply put, high frequencies are projected towards the listener like a spotlight.

Directivity increases with increasing signal frequency, reaching a maximum at the highest frequencies. It is the directionality that determines the main importance of HF waves in the formation of a stereo image.

The second characteristic feature of HF is the ability for multiple reflections from solid surfaces, like a rebounding bullet or a billiard ball, which, in turn, causes their easy dispersion (diffusion).

Third feature - easy absorption even thin soft surfaces, such as, for example, curtains.

It is thanks to the directionality and ability to reflect that high frequencies, as noted above, take an active part in the formation of the reverberation pattern.

Low frequency or bass waves (long wavelengths).

So, the behavior of low frequencies in a closed space looks like a purely wave process, which is based on interference, that is, the process of addition (superposition) of sound waves emanating from absolutely all low frequency sources located in the room, as well as many low frequency reflections from the walls , floor and ceiling of this room.

This is due to the fact that, unlike mid and high frequency waves, which are directional, bass waves spread evenly in all directions like spheres diverging from the radiating center. Thus, LF sound waves are omnidirectional, which is why it is impossible to determine the location of the woofer with your eyes closed.

This property of low-frequency waves explains their inability to participate in the formation of a stereo image.

In addition, thanks to their long wavelength and high energy, low-frequency waves are capable of not only bending around an obstacle, but also, partially being reflected, “passing” through even concrete walls (this is exactly the case when your distant neighbors in a “high-rise building” hear low-frequency "buzz" while you listen to music).

Thus, unlike high frequencies, which are easily reflected from hard surfaces, bass waves are reflected much worse, being partially absorbed and partially passing through an obstacle, and with decreasing frequency they increasingly lose their ability to reflect and prefer to “go ahead”.

And LF waves “are able” to “leak” out of a room through open window and door openings, and also easily penetrate glass, as if it were not there at all.

Taking into account all the above points, and also taking into account the fact that the lengths of low-frequency waves are commensurate with the linear dimensions of the room (length, width and height), it becomes clear why the behavior of bass waves is mainly influenced by the parameters of the room.

If the wavelength of the sound signal is twice as large as one of the linear dimensions of the room, then at its frequency between a given pair of walls the most formidable and difficult to suppress acoustic phenomenon occurs, literally “killing” the sound - air volume resonance.

Subjectively, this is expressed in the amplification of the signal of this particular frequency in relation to the level of other frequencies and the appearance of a booming sound.

Low-frequency resonances and standing waves occur between two parallel surfaces (for example, between the front and rear walls or between side walls, or between the floor and ceiling) when a sound wave with the corresponding frequency is excited in a given room.

Moreover, it does not matter at all what will excite this wave: playing music, playing musical instrument, timbre of voice during a conversation, sounds of communications or passing vehicles, operation of electrical appliances, etc.).

Low-frequency sound waves travel omnidirectionally (“...we can't localize bass below 80 Hz...” - Anthony Grimani) and they have enormous energy. The lowest of them, bass frequencies, are able to pass through any obstacles with virtually no reflection.

As the frequency increases, their reflective ability increases and their penetrating ability decreases.

“It is believed that sound travels in a straight line, like any waves. But this is true only for a wide space devoid of obstacles. In reality, the movement of sound waves is immeasurably more complex. They collide with obstacles and with each other, and sometimes spread, forming vortices, along indescribable trajectories.

In my opinion, those who work in audio engineering need to have spatial awareness in order to clearly imagine visual images sound waves and their behavior, which cannot be explained based only on the theory of electricity.

It seems that to this day, a huge number of factors influencing sound reproduction remain unexplored, challenging all the accumulated knowledge and experience of sound engineers. The more I think about it, the more I realize that the world of sound is much deeper than we can imagine."

The reflection of sound waves from the interface between two media is of very great practical importance. Let us consider an experiment illustrating the laws of sound reflection (§ 24.19).

Place a watch at the bottom of a glass beaker. If you stand at such a distance from the beaker that the clock cannot be heard, and then place a glass plate over the hole of the beaker, as shown in Fig. 25.7, then the ticking of the clock will be heard. By changing the angle of the plate and the position of the ear, you can make sure that the angle of incidence is equal to the angle of reflection.

An interesting case of sound reflection occurs when the reflecting surface is located perpendicular to the direction of wave propagation. In this case, the sound wave, after reflection, returns back to its source. The return of a sound wave to its source after reflection is called an echo.

It turns out that a person retains a sound sensation for

0.1 s after the tympanic membrane in the ear stops vibrating. This means that at a short distance from the reflecting surface to the ear, the echo will merge with the main sound and only slightly lengthen its duration. This means that the echo can be heard separately from the main sound only at a sufficiently large distance to the obstacle.

This allows you to determine the distance from the sound source to the reflective surface. Let the distance from the sound source A to the reflecting surface B be equal to I (Fig. 25.8). If the time between the departure of a sound signal from point A and its return to the same point is equal and the speed of sound is equal, then where does

It is clear that the sound signal must be short-term, since with a long signal the echo will merge with the main sound and the time t cannot be determined. (Show that at a speed of sound in air of 344 m/s (at 20°C), the echo will be heard separately from the main sound if the distance to the reflecting surface exceeds 17.2 m.)

In a closed room, sound is repeatedly reflected from the walls, which increases the duration of the sound after the sound source stops.

The residual sound in a closed room is called reverberation. For small rooms, the reverberation time should be about 1 s. Reverberation time greatly influences the sound quality in concert halls, since if the reverberation time is too long, the music cannot be listened to, and if the reverberation time is too short, the sounds will become dull and abrupt.

At the interface between two media, sound is not only reflected, but also absorbed when penetrating into another medium. The energy of sound waves is partially converted into the energy of chaotic movement of the molecules of the medium. For example, a plaster wall absorbs about 8% of the energy of sound waves, and a carpet about 20%. This explains the fact that in a room filled with things the sound is dull, but in an empty room the sound is loud.

SOUND REFLECTION

A phenomenon that occurs when sound falls on the interface between two elastic media and consists of the formation of waves propagating from the interface into the same medium, sound scattering or sound diffraction.
The incident wave causes interfaces between the media, as a result of which reflected and refracted waves arise. Their structure and intensity must be such that on both sides of the interface the particle velocities and elastic stresses acting at the interface are equal. The boundary conditions on the free surface are that the elastic stresses acting on this surface are equal to zero.
Reflected waves can have the same type of polarization as the incident wave, or they can have a different polarization. In the latter case, they talk about the transformation, or conversion, of modes during reflection or refraction. Reflection of plane waves A special role is played by the reflection of plane waves, since plane waves, when reflected and refracted, remain plane, and an arbitrary shape can be considered as a reflection of a set of plane waves. The number of reflected and refracted waves that arise is determined by the nature of the elastic properties of the media and the number of acoustic waves. branches existing in them. Due to the boundary conditions, the projections onto the interface plane of the wave vectors of the incident, reflected and refracted waves are equal to each other (Fig. 1).

Rice. 1. Scheme of reflection and refraction of a plane sound wave at a flat interface.

This implies the laws of reflection and refraction, i, reflectedk r and refracted k t waves and normal NN" to the interface lie in the same plane (the plane of incidence); 2) the ratio of the sines of the angles of incidence of reflection and refraction to the phase velocities c i, and the corresponding waves are equal to each other:
(the indices indicate the polarization of reflected and refracted waves). In isotropic media, where the directions of the wave vectors coincide with the directions of sound rays, the laws of reflection and refraction take the usual form of Snell's law. In anisotropic media, the laws of reflection determine only the directions of wave normals; how refracted or reflected rays will propagate depends on the direction of the radial velocities corresponding to these normals.
At sufficiently small angles of incidence, all reflected and refracted waves are plane waves that carry away the energy of the incident radiation from the interface. However, if for k.-l. refracted wave greater speed c i incident wave, then for angles of incidence, large. n. critical angle =arcsin, the normal component of the wave vector of the corresponding refracted wave becomes imaginary, 2. However, the incidence of a wave on the interface at an angle greater than the critical one may not lead to total reflection, since the incident radiation can penetrate into the 2nd medium in the form of waves of a different polarization.
Critical the angle also exists for reflected waves if, at O.Z. mode conversion occurs and the wave resulting from the conversion is greater than the speed c i incident wave. For angles of incidence less than critical. angle, part of the incident energy is carried away from the boundary in the form of a reflected wave with polarization; such a wave turns out to be inhomogeneous, attenuated deep into medium 1, and does not take part in the transfer of energy from the interface. For example, critical angle = arcsin( c t/c L) occurs when transverse acoustic is reflected. waves T from the boundary of an isotropic solid and its conversion into a longitudinal wave L (with t and C L - velocities of transverse and longitudinal sound waves, respectively).
The amplitudes of reflected and refracted waves in accordance with the boundary conditions are linearly expressed through the amplitude A i incident wave, just as these quantities in optics are expressed through the amplitude of the incident electric magnetic field. waves using Fresnel formulas. The reflection of a plane wave is quantitatively characterized by amplitude coefficients. reflections, which are the ratio of the amplitudes of the reflected waves to the amplitude of the incident one: = Amplitude coefficients. reflections in the general case are complex: their modules determine the abs relations. amplitude values, and phases specify the phase shifts of reflected waves. The amplitude coefficients are determined similarly. passing The redistribution of incident radiation energy between reflected and refracted waves is characterized by a coefficient. reflection and transmission in intensity, which are the ratios of the normal to the interface components of the time-averaged energy flux densities in the reflected (refracted) and incident waves:

where are the sound intensity in the corresponding waves, and are the densities of the contacting media. The balance of energy supplied to the interface and carried away from it is reduced to the balance of the normal components of energy flows:

Coef. reflections depend both on acoustics. .Character of angle dependence is determined by the presence of critical angles, as well as angles of zero reflection, when falling under them, a reflected wave with polarization is not formed.

O. z. at the interface of two liquids. Naib. simple picture of O. z. occurs at the interface between two fluids. In this case, there is no wave conversion, and reflection occurs according to the mirror law, and the coefficient. reflection is equal

where and c 1.2 - density and speed of sound in adjacent media . And 2. If the speed of sound for an incident wave is greater than the speed of sound for a refracted wave ( With 1 c 2), then critical. there is no angle.

with normal wave incidence on the interface up to the value R = - 1 with sliding fall If acoustic. r 2 from 2 Wednesday 2 more impedance of the medium 1 , then at the angle of incidence

coefficient reflection vanishes and the all-incident completely passes into the medium 2.
When from 1<с 2 ,возникает критический угол =arcsin(c 1 /c 2). At<коэф. отражения - действительная величина; фазовый между падающейи отражённой волнами отсутствует. Величина коэф. отражения меняется отзначения R0 with a normal drop to R= 1 angle of incidence equal to critical. Zero reflection may also occur in this case, if for acoustic impedances of the media, the inverse inequality holds The angle of zero reflection is still determined by expression (6). For angles of incidence greater than the critical one, there is a complete internal reflection: and incident radiation deep into the medium 2 does not penetrate. In the environment 2, however, the field of the reflected wave is formed as a result of the interference of two fields: the specularly reflected wave and the wave, 1 inhomogeneous wave arising in the medium 2. In the reflection of non-plane (for example, spherical) waves, such a re-emitted wave is actually observed in experiment in the form of the so-called. side wave (see waves, sectionReflection and ).

O. z. from the solid boundary. The nature of reflection becomes more complicated if the reflector is a solid body. When With in liquid there are less longitudinal velocities L and transverse With t of sound in a solid body, when reflected at the boundary of a liquid with a solid body, two critical conditions arise. angle: longitudinal =arcsin ( s/s L) and transverse =arcsin ( s/s T ). At the same time, since always with L > with T . At angles of incidence coefficient. reflection is valid (Fig. 2). Incident radiation penetrates the solid in the form of both longitudinal and transverse refracted waves. With normal incidence of sound in a solid body, only the value appears R 0 is determined by the ratio of longitudinal acoustic. impedances of liquid and solid are similar to f-le (5) (- density of liquid and solid).

Rice. 2. Dependence of the modulus of sound reflection coefficient | R | (solid line) and its phases (dashed-dotted line) at the boundary of the liquid and solid body from the angle of incidence .

At coefficient and part of the incident radiation penetrates deep into the solid body in the form of a refracted transverse wave. Therefore for<<величина лишь при поперечная волна не образуется и |R|= 1. The participation of a non-uniform longitudinal wave in the formation of reflected radiation causes, as at the boundary of two liquids, a phase shift in the reflected wave. When there is a complete internal reflection:1. In a solid body near the boundary, only inhomogeneous waves are formed that decay exponentially into the body. The phase shift of the reflected wave for angles is associated mainly with the excitation of the leaking fluid at the interface Rayleigh waves. Such a wave arises at the boundary of a solid with a liquid at angles of incidence close to the Rayleigh angle = arcsin ( s/s R), Where C R - Rayleigh wave speed on the surface of a solid body. Propagating along the interface, the leaking wave is completely re-emitted in .
If WithWith T . full internal There is no reflection at the boundary of a liquid with a solid: incident radiation penetrates at any angle of incidence, at least in the form of a transverse wave. Total reflection occurs when a sound wave falls below a critical point. angle or sliding fall. When c>c L coefficient. reflection of a real, O. Z., propagating in a solid body. When sound propagates in an isotropic solid, the max. The simple character is the reflection of shear waves, the direction of oscillations in which is parallel to the interface plane. There is no mode conversion during reflection or refraction of such waves. When falling on a free boundary or interface with a liquid, such a wave is completely reflected ( R= 1) according to the law of mirror reflection. At the interface between two isotropic solids, along with a specularly reflected wave in the medium 2 a refracted wave with polarization is formed. When a transverse wave, polarized in the plane of incidence, falls on the free surface of the body, both a reflected wave of the same polarization and a longitudinal wave appear at the boundary. ,smaller critical angle = = arcsin ( c T /c L), coefficient reflections R T and R L - purely real: reflected waves leave the boundary exactly in phase (or out of phase) with the incident wave. At the boundary, only the specularly reflected transverse wave leaves; An inhomogeneous longitudinal wave is formed near the free surface.
Coef. reflection becomes complex. If the boundary of a solid body is in contact with a liquid, then when waves (longitudinal or transverse) are reflected, 2. It also lies in the plane of incidence.

ABOUT . h. at the interface of anisotropic media. O. z. at the crystalline interface. environment is complex. and reflected and refracted waves in this case are themselves functions of the angles of reflection and refraction (see. Crystal acoustics); Therefore, even determining angles from a given angle of incidence faces serious math problems. difficulties. If the cross sections of the surfaces of the wave vectors by the plane of incidence are known, then the graphic is used. method for determining angles and ends of wave vectors k r and k t lie perpendicular NN", drawn to the interface through the end of the wave vector k i incident wave, at the points where this perpendicular intersects the dif. cavities of wave vector surfaces (Fig. 3). The number of reflected (or refracted) waves actually propagating from the interface into the depths of the corresponding medium is determined by how many cavities the perpendicular intersects NN". If the intersection with a k.-l. cavity is absent, this means that the wave of the corresponding polarization turns out to be inhomogeneous and does not transfer energy from the boundary. Perpendicular NN" can cross the same cavity several times. points (points a 1 and a 2 in Fig. 3). From the possible positions of the wave vector k r (or k t) the only waves that are actually observed correspond to those for which the radial velocity vector is

Rice. 3. Graphical method for determining the angles of reflection and refraction at the interface between crystalline media 1 And 2.L, FT And ST- surfaces of wave vectors for quasi-longitudinal ones. As a rule, reflected (refracted) waves belong to different types. acoustic branches fluctuations. However, in crystals it means. anisotropy, when the surface of the wave vectors has concave sections (Fig. 4), reflection is possible with the formation of two reflected or refracted waves belonging to the same branch of oscillations.
Experimentally, finite beams of sound waves are observed, the directions of propagation of which are determined by radial velocities. NN" to the interface. In particular, the reflected one can lie in the plane of incidence on the same side of the normal N, the same as the incident beam. The limiting case of this possibility is the superposition of a reflected beam on an incident beam at an oblique incidence of the latter.

Rice. 4. Reflection of an acoustic wave incident on the free surface of the crystal with the formation of two reflected waves of the same polarization: A- determination of wave vectors of reflected waves (with g- radial velocity vectors); b- diagram of reflection of sound beams of finite cross-section.

The influence of attenuation on the nature of O. z..Coef. reflections and transmissions do not depend on the frequency of sound if the attenuation of sound in both boundary media is negligible. Noticeable attenuation leads not only to the frequency dependence of the coefficient. reflections R, but you also distort its dependence on the angle of incidence, especially near the critical point. corners (Fig. 5, A). When reflected from the interface between a liquid and a solid, attenuation effects significantly change the angular dependence R at angles of incidence close to the Rayleigh angle (Fig. 5 B). At the boundary of media with negligible attenuation at such angles of incidence, | R|= 1 (curve 1 in Fig. 5, b). The presence of attenuation leads to the fact that | R|becomes less than 1, and a minimum is formed nearby | R|(curves 2 - 4). As the frequency increases and the corresponding increase in coefficient. attenuation, the depth of the minimum increases, f 0, called. zero reflection frequency, min. meaning | R|will not vanish (curve 3, Fig.5, b). A further increase in frequency leads to a broadening of the minimum (curve 4 ) the influence of attenuation effects on O.Z. for almost any angle of incidence (curve 5). A decrease in the amplitude of the reflected wave compared to the amplitude of the incident wave does not mean that the incident radiation penetrates the solid. It is associated with the absorption of the outgoing Rayleigh wave, which is excited by the incident radiation and participates in the formation of the reflected wave. When sound frequency f equal to frequency f 0, all the energy of the incident wave is dissipated at the interface.

Rice. 5. Angular dependence | R|at the water-steel boundary, taking into account attenuation: A- general nature of the angular dependence | R|; solid line - without taking into account losses, dashed line - the same with attenuation taken into account; b- angular dependence | R near the Rayleigh angle at different values of absorption of transverse waves in steel at a wavelength. Curves 1 - 5 corresponds to an increase in this parameter from a value of 3 x 10 -4 (curve 1 ) to value = 1 (curve 5) due to a corresponding increase in the frequency of the incident ultrasonic radiation.

O. z. from layers and plates.ABOUT. h. from a layer or plate is resonant in nature. Reflected and transmitted waves are formed as a result of multiple re-reflections of waves at the boundaries of the layer. In the case of a liquid layer, the incident wave penetrates the layer at a refraction angle determined from Snell's law. Due to re-reflections, longitudinal waves arise in the layer itself, propagating in the forward and reverse directions at an angle to the normal drawn to the boundaries of the layer (Fig. 6, A). The angle is the angle of refraction corresponding to the angle of incidence on the layer boundary. If the speed of sound in the layer With 2 more speed of sound With 1 in the surrounding liquid, then the system of reflected waves arises only when the angle of total internal is less than. reflections = arcsin(c 1 /c 2). However, for sufficiently thin layers, a transmitted wave is also formed at angles of incidence greater than the critical one. In this case the coefficient reflection from the layer turns out to be abs. value less than 1. This is due to the fact that when in the layer near the boundary on which a wave falls from the outside, a non-uniform wave arises, decaying exponentially into the depth of the layer. If the layer thickness d is less than or comparable to the depth of penetration of the inhomogeneous wave, then the latter disturbs the opposite boundary of the layer, as a result of which the transmitted wave is emitted from it into the surrounding liquid. This wave percolation phenomenon is analogous to particle percolation in quantum mechanics.
Coef. layer reflections

where is the normal component of the wave vector in the layer, the axis z- perpendicular to the layer boundaries, R 1 and R 2 - coefficient O. z. represents a periodic audio frequency function f and layer thickness d. When there is wave penetration through the layer, | R | with increasing f or d monotonically tends to 1.

Rice. 6. Reflection of a sound wave from a liquid layer: A - reflection circuit; 1 - surrounding fluid; 2- layer; b - dependence of the modulus of the reflection coefficient | R| angle of incidence.

How does the angle of incidence function matter? R | has a system of maxima and minima (Fig. 6, b). If there is the same liquid on both sides of the layer, then at the minimum points R= 0. Zero reflection occurs when the phase shift across the layer thickness is equal to an integer number of half-cycles

and the waves emerging into the upper medium after two successive re-reflections will be in antiphase and cancel each other out. On the contrary, all reflected waves enter the lower medium with the same phase, and the amplitude of the transmitted wave turns out to be maximum. transmission occurs when an integer number of half-waves fits across the layer thickness: d = Where . =1,2,3,..., - sound wavelength in the layer material; Therefore, layers for which condition (8) is satisfied are called. half-wave Relationship (8) coincides with the condition for the existence of a normal wave in a free liquid layer. Because of this, complete transmission through the layers occurs when the incident radiation excites one or another normal wave in the layer. Due to the contact of the layer with the surrounding liquid, the normal wave is leaky: during its propagation, it completely re-radiates the energy of the incident radiation into the lower medium.
When the liquids on opposite sides of the layer are different, the presence of a half-wave layer has no effect on the incident wave: coefficient. reflection from the layer is equal to the coefficient. reflections from the boundaries of these liquids directly through them. contact. In addition to half-wave layers in acoustics, as in optics, the so-called. quarter-wave layers of thickness satisfy the condition ( n= 1,2,...).Selecting the acoustics accordingly. impedance of the layer, you can get zero reflection from the layer of a wave with a given frequency f at a certain angle of its incidence on the layer. Such layers are used as antireflective acoustic layers.
For the reflection of a sound wave from an infinite solid plate immersed in a liquid, the nature of the reflection described above for a liquid layer will remain in general terms. During reflections in the plate, in addition to longitudinal ones, shear waves will also be excited. The angles and , under which longitudinal and transverse waves propagate respectively in the plate, are related to the angle of incidence by Snell’s law. Angle and frequency dependence| R| will represent, as in the case of reflection from a liquid layer, a system of alternating maxima and minima. Complete transmission through the plate occurs when the incident radiation excites one of the normal waves, which are leaky waves. Lamb waves. Resonant character of O. z. from a layer or plate is erased as the difference between their acoustics decreases. properties from the properties of the environment. Increase in acoustic and | R(fd)|.

Reflection of non-plane waves. In reality, only non-plane waves exist; their reflection can be reduced to the reflection of a set of plane waves. Monochromatic a wave with a wavefront of arbitrary shape can be represented as a set of plane waves with the same circular frequency, but with different directions of the wave vector k. Basic characteristic of incident radiation is its spatial - set of amplitudes A(k)plane waves, which together form an incident wave. Abs. the value of k is determined by the frequency, so they are not independent. When reflected from a plane z= 0 normal component k z specified by tangential components k x , k y: k z=Each wave that is part of the incident radiation falls at the interface at its own angle and is reflected independently of other waves. Field F( r) of the reflected wave arises as a superposition of all reflected plane waves and is expressed through the spatial spectrum of the incident radiation A(k x , k y)icoeff. reflections R(k x , k y):

Integration extends to a region of arbitrarily large values k x And k y . If the spatial spectrum of incident radiation contains (as when reflecting a spherical wave) components with k x(or k y), large, then in the formation of a reflected wave in addition to waves with real k z Inhomogeneous waves also take part, for which k, - pure value. This approach, proposed in 1919 by G. Weyl (N. Weyl) and which received its further development in the concepts of Fourier optics, gives the following. description of the reflection of a wave of arbitrary shape from a flat surface.
When considering O. z. A radiation approach is also possible, which is based on the principles geometric acoustics. Incident radiation is considered as a set of rays interacting with the interface. In this case, it is taken into account that the incident rays are not only reflected and refracted in the usual way, obeying Snell’s laws, but also that some of the rays incident on the interface at certain angles excite. n. lateral waves, as well as leaky (Rayleigh, etc.) or leaky waveguide (Lamb waves, etc.). Propagating along the interface, such waves are again re-emitted into the medium and participate in the formation of the reflected wave. For practice basic. reflection is spherical. waves collimated by acoustic waves. finite-section beams and focused sound beams.

Reflection of spherical waves. The reflection pattern is spherical. wave created in liquid I by a point source ABOUT, depends on the relationship between the speeds of sound With 1 and from 2 to contacting liquids I and II (Fig. 7). If c t > c 2, then critical. There is no angle and reflection occurs according to geometric laws. acoustics. In medium I, a reflected spherical particle appears. O". forming an imaginary image of the source, and the reflected wave is part of a sphere centered at the point ABOUT".

Rice. 7. Reflection of a spherical wave at the interface between two liquids: ABOUT And ABOUT" - actual imaginary sources; 1 - front of a reflected spherical wave; 2 - front of the refracted wave; 3 - side wave front.

When c 2 l there is a critical angle in medium I in addition to the reflected spherical. wave, another component of reflected radiation arises. Rays incident on the interface under the critical angle excite wave II in the medium, the edges propagate at a speed With 2 along the interface surface and is re-emitted into medium I, forming the so-called. Oh along OA and then transferred again to environment I in decomposition. points of the interface from the point . dots WITH, in which at this moment the front of the refracted wave is located. NE, inclined to the boundary at an angle and extending to a point IN, where it meets the front of the mirror-reflected spherical. waves. In space, the front of a lateral wave is the surface of a truncated cone that appears when a segment rotates NE aroundstraight OO". When reflected, spherical. waves in a liquid from the surface of a solid body are similar to conic. the wave is formed due to the excitation of a leaky Rayleigh wave at the interface. Reflection spherical waves - one of the main experiments. methods of geoacoustics, seismology, hydroacoustics and ocean acoustics.

Reflection of finite-section acoustic beams. Reflection of collimated sound beams, the wavefront of which is mainly part of the beam is close to flat, occurs for most angles of incidence as if a plane wave is reflected. When the beam is reflected, or to the Rayleigh angle, along with specular reflection, an effect occurs. lateral or leaky Roleigh wave. The field of the reflected beam in this case is a superposition of the specularly reflected beam and re-emitted waves. Depending on the width of the beam, elastic and viscous properties of the adjacent media, either a lateral (parallel) shift of the beam in the interface plane (the so-called Schoch shift) occurs (Fig. 8), or a significant broadening of the beam and the appearance of a thin

Rice. 8. Lateral displacement of the beam in reflection: 1 - falling beam; 2 - specularly reflected beam; 3- actual reflected beam.

structures. When the beam is incident at a Rayleigh angle, the nature of the distortions is determined by the ratio between the beam width . iradiac. damping of the leaky Rayleigh wave

where is the sound wavelength in the liquid, A - a numerical factor close to unity. If the width of the beam is significantly greater than the length of the radiation. Attenuation occurs only when the beam shifts along the interface by an amount. In the case of a narrow beam, due to the re-emission of the leaking surface wave, the beam broadens significantly and ceases to be symmetrical (Fig. 9). Inside the region occupied by the specularly reflected beam, as a result of interference, a zero minimum amplitude appears and the beam splits into two parts. Non-specular reflection of collimirs.

Rice. 9. Reflection of a sound beam of finite cross-section falling from a liquid G onto the surface of a solid body T at a Rayleigh angle: 1 - incident beam; 2 - reflected beam; A - zero amplitude region; b- area of the beam tail.

In the latter case, the non-specular character of the reflection is due to the excitation of leaky waveguide modes in the layer or plate. Significant role lateral and leaky waves play when focused ultrasonic beams are reflected. In particular, these waves are used in microscopyacoustic for the formation of acoustic images and holding quantities, Lit.: 1) Brekhovskikh L.M., Waves in layered media, 2nd ed., M., 1973; 2) Landau L.D., Lifshits E.M., Hydrodynamics, 4th ed., M., 1988; 3) Brekhovskikh L.M., Godin O.A., Acoustics of layered media, V. M. Levin.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Chief Editor A. M. Prokhorov. 1988 .

If a sound wave does not encounter obstacles in its path, it propagates evenly in all directions. But not every obstacle becomes a barrier for her.

Having encountered an obstacle in its path, sound can bend around it, be reflected, refracted or absorbed.

Sound diffraction

We can talk to a person standing around the corner of a building, behind a tree or behind a fence, although we cannot see him. We hear it because sound is able to bend around these objects and penetrate into the area behind them.

The ability of a wave to bend around an obstacle is called diffraction .

Diffraction occurs when the sound wavelength exceeds the size of the obstacle. Low frequency sound waves are quite long. For example, at a frequency of 100 Hz it is equal to 3.37 m. As the frequency decreases, the length becomes even greater. Therefore, a sound wave easily bends around objects comparable to it. The trees in the park do not interfere with our hearing of sound at all, because the diameters of their trunks are much smaller than the length of the sound wave.

Thanks to diffraction, sound waves penetrate through cracks and holes in an obstacle and propagate behind them.

Let's place a flat screen with a hole in the path of the sound wave.

In the case where the sound wavelength ƛ much larger than the hole diameter D , or these values are approximately equal, then behind the hole the sound will reach all points in the area that is behind the screen (sound shadow area). The front of the outgoing wave will look like a hemisphere.

If ƛ is only slightly smaller than the diameter of the slit, then the main part of the wave propagates straight, and a small part diverges slightly to the sides. And in the case when ƛ much less D , the whole wave will go in the forward direction.

Sound reflection

If a sound wave hits the interface between two media, different options for its further propagation are possible. Sound can be reflected from the interface, can move to another medium without changing direction, or can be refracted, that is, move, changing its direction.

Suppose an obstacle appears in the path of a sound wave, the size of which is much larger than the wavelength, for example, a sheer cliff. How will the sound behave? Since it cannot go around this obstacle, it will be reflected from it. Behind the obstacle is acoustic shadow zone .

The sound reflected from an obstacle is called echo .

The nature of the reflection of the sound wave may be different. It depends on the shape of the reflective surface.

Reflection called a change in the direction of a sound wave at the interface between two different media. When reflected, the wave returns to the medium from which it came.

If the surface is flat, sound is reflected from it in the same way as a ray of light is reflected in a mirror.

Sound rays reflected from a concave surface are focused at one point.

The convex surface dissipates sound.

The effect of dispersion is given by convex columns, large moldings, chandeliers, etc.

Sound does not pass from one medium to another, but is reflected from it if the densities of the media differ significantly. Thus, sound that appears in water does not transfer into the air. Reflected from the interface, it remains in the water. A person standing on the river bank will not hear this sound. This is explained by the large difference in the wave impedances of water and air. In acoustics, wave impedance is equal to the product of the density of the medium and the speed of sound in it. Since the wave resistance of gases is significantly less than the wave resistance of liquids and solids, when a sound wave hits the boundary of air and water, it is reflected.

Fish in water do not hear the sound appearing above the surface of the water, but they can clearly distinguish the sound, the source of which is a body vibrating in the water.

Refraction of sound

Changing the direction of sound propagation is called refraction . This phenomenon occurs when sound travels from one medium to another, and its speed of propagation in these environments is different.

The ratio of the sine of the angle of incidence to the sine of the angle of reflection is equal to the ratio of the speeds of sound propagation in media.

Where i - angle of incidence,

r – angle of reflection,

v 1 – speed of sound propagation in the first medium,

v 2 – speed of sound propagation in the second medium,

n – refractive index.

The refraction of sound is called refraction .

If a sound wave does not fall perpendicular to the surface, but at an angle other than 90°, then the refracted wave will deviate from the direction of the incident wave.

Refraction of sound can be observed not only at the interface between media. Sound waves can change their direction in a heterogeneous medium - the atmosphere, the ocean.

In the atmosphere, refraction is caused by changes in air temperature, speed and direction of movement of air masses. And in the ocean it appears due to the heterogeneity of the properties of water - different hydrostatic pressure at different depths, different temperatures and different salinity.

Sound absorption

When a sound wave encounters a surface, part of its energy is absorbed. And how much energy a medium can absorb can be determined by knowing the sound absorption coefficient. This coefficient shows what part of the energy sound vibrations absorbs 1 m 2 of obstacles. It has a value from 0 to 1.

The unit of measurement for sound absorption is called sabin . It got its name from the American physicist Wallace Clement Sabin, founder of architectural acoustics. 1 sabin is the energy that is absorbed by 1 m 2 of surface, the absorption coefficient of which is 1. That is, such a surface must absorb absolutely all the energy of the sound wave.

Reverberation

Wallace Sabin

The property of materials to absorb sound is widely used in architecture. While studying the acoustics of the Lecture Hall, part of the Fogg Museum, Wallace Clement Sabin concluded that there was a relationship between the size of the hall, the acoustic conditions, the type and area of sound-absorbing materials and reverberation time .

Reverberation call the process of reflection of a sound wave from obstacles and its gradual attenuation after the sound source is turned off. In an enclosed space, sound can be reflected repeatedly from walls and objects. As a result, various echo signals arise, each of which sounds as if separately. This effect is called reverberation effect .

The most important characteristic of the room is reverberation time , which Sabin entered and calculated.

Where V – volume of the room,

A – general sound absorption.

Where a i – sound absorption coefficient of the material,

S i - area of each surface.

If the reverberation time is long, the sounds seem to “wander” around the hall. They overlap each other, drown out the main source of sound, and the hall becomes booming. With a short reverberation time, the walls quickly absorb sounds and they become dull. Therefore, each room must have its own exact calculation.