Fundamentals of sound propagation. sound reflection

Let us put a flat plate in the path of waves in a water bath, the length of which is large compared to the wavelength. We will see the following. Behind the plate, a region is obtained in which the surface of the water remains almost at rest (Fig. 83). In other words, the plate creates a shadow - a space where the waves do not penetrate. In front of the plate, one can clearly see how the waves are reflected from it, i.e., the waves incident on the plate create waves coming from the plate. These reflected waves are in the form of concentric arcs, running as if from a center lying behind the plate. In front of the plate there is a kind of grid of primary waves incident on the plate and reflected waves coming from it towards the incident ones.

How does the direction of wave propagation change when it is reflected?

Let's see how a plane wave is reflected. Let us denote the angle formed by the perpendicular to the plane of our “mirror” (plate) and the direction of propagation of the incident wave through (Fig. 84), and the angle formed by the same perpendicular and the direction of propagation of the reflected wave through. Experience shows that for any position of the "mirror", i.e., the angle of reflection of the wave from the reflecting plane is equal to the angle of incidence.

Rice. 83. Shadow cast by a large plate

Rice. 84. The angle of reflection is equal to the angle of incidence

This law of reflection is a general wave law, i.e., it is valid for any waves, including both sound and light. The law remains valid for spherical (or annular) waves, as can be seen from Fig. 85. Here the angle of reflection at different points of the reflecting plane is different, but at each point it is equal to the angle.

Rice. 85. The law of reflection is fulfilled at every point of the reflecting plane

The reflection of waves from obstacles is one of the most common phenomena. The well-known echo is due to the reflection of sound waves from buildings, hills, forests, etc. If sound waves reach us successively reflected from a series of obstacles, then a multiple echo is obtained. Thunder rolls have the same origin. This is a multiple repetition of a very strong "crack" of a huge electric spark - lightning. The location methods mentioned in § 35 were based on the reflection of electromagnetic waves and elastic waves from obstacles. Especially often we observe the phenomenon of reflection on light waves.

The reflected wave is always weakened to some extent compared to the incident wave. Part of the energy of the incident wave is absorbed by the body from the surface of which the reflection occurs. Sound waves are well reflected by hard surfaces (plaster, parquet) and much worse by soft surfaces (carpets, curtains, etc.).

Any sound does not stop immediately after its source is silent, but fades gradually. The reflection of sound in rooms causes an after-sound phenomenon called reverberation. In empty rooms, the reverberation is high; we observe a kind of boom. If there are many absorbing surfaces in the room, especially soft ones (upholstered furniture, people's clothes, curtains, etc.), then boominess is not observed. In the first case, a large number of sound reflections are obtained before the energy of the sound wave is almost completely absorbed, in the second, the absorption occurs much faster.

Reverberation significantly determines the sound quality of a room and plays a large role in architectural acoustics. For a given room (audience, hall, etc.) and a given kind of sound (speech, music), absorption must be selected specifically. It should not be too large so that a dull, “dead” sound is not obtained, but also not too small so that a long reverberation does not disturb the intelligibility of speech or the sound of music.

Room acoustics (geometric theory)

Geometric (ray) theory

Basic provisions. The geometric (ray) theory of acoustic processes in rooms is based on the laws of geometric optics. The movement of sound waves is considered similar to the movement of light rays. In accordance with the laws of geometric optics, when reflected from mirror surfaces, the angle of reflection b is equal to the angle of incidence a, and the incident and reflected rays lie in the same plane. This is true if the dimensions of the reflecting surfaces are much larger than the wavelength, and the dimensions of the surface irregularities are much smaller than the wavelength.

The nature of the reflection depends on the shape of the reflecting surface. When reflected from a flat surface (Fig. 7, a), an imaginary source I "appears, the place of which is felt by ear, just as the eye sees an imaginary light source in a mirror. Reflection from a concave surface (Fig. 7, b) leads to focusing of the rays at point I. Convex surfaces (columns, pilasters, large moldings, chandeliers) scatter sound (Fig. 7, c).

The role of initial reflections. Important for auditory perception is the delay of reflected sound waves. The sound emitted by the source reaches an obstacle (for example, a wall) and is reflected from it. The process is repeated many times with the loss of part of the energy with each reflection. The first delayed pulses, as a rule, arrive at the listeners' seats (or at the microphone location) after reflection from the ceiling and walls of the hall (studio).

Due to the inertia of hearing, a person has the ability to preserve (integrate) auditory sensations, combine them into a general impression if they last no more than 50 ms (more precisely, 48 ms). Therefore, a useful sound that reinforces the original sound includes all waves that reach the ear within 50 ms after the original sound. A delay of 50 ms corresponds to a path difference of 17 m. Concentrated sounds that arrive later are perceived as an echo. Reflections from obstacles that fit within the specified time interval are useful, desirable, as they increase the sensation of loudness by values up to 5 - 6 dB, improve the sound quality, giving the sound "liveness", "plasticity", "voluminous". Such are the aesthetic assessments of musicians.

Studies of the initial reflections by acoustic modeling were carried out at the Research Film and Photo Institute (NIKFI) under the direction of A. I. Kacherovich. The influence of shape, volume, linear dimensions, placement of sound-absorbing materials on the sound quality of speech and music was studied. Interesting results have been obtained.

The direction of arrival of the initial reflections plays a significant role. If the delayed signals, i.e. Since all early reflections arrive at the listener from the same direction as the direct signal, the ear almost does not distinguish the difference in sound quality compared to the sound of only direct sound. There is an impression of a "flat" sound, devoid of volume. Meanwhile, even the arrival of only three delayed signals in different directions, despite the absence of a reverberation process, creates the effect of spatial sound. The quality of the sound depends on which directions and in what sequence the delayed sounds come. If the first reflection comes from the front side, the sound deteriorates, and if from the rear side, it deteriorates sharply.

The delay time of the initial reflections with respect to the moment of arrival of the direct sound and with respect to each other is quite significant. The duration of the delay must be different for the best sounding of speech and music. Good speech intelligibility is achieved if the first delayed signal arrives no later than 10 - 15 ms after the direct one, and all three should occupy a time interval of 25 - 35 ms. When playing music, the best sense of spatiality and "transparency" is achieved if the first reflection arrives at the listener no earlier than 20 ms and no later than 30 ms after the direct signal. All three delayed signals should be located in the time interval of 45 - 70 ms. The best spatial effect is achieved if the levels of the delayed initial signals differ slightly from each other and from the level of the direct signal.

When connected to the structure of the initial reflections (first, second, third) of the rest of the echo, the most favorable sound is obtained when the second part of the process begins after all discrete reflections. Connecting the process of reverberation (response) immediately after the direct signal degrades the sound quality.

When providing the optimal structure of the initial (early) reflections, the sound of the music remains good even with a significant (by 10 - 15%) deviation of the reverberation time from the recommended one. Achieving the optimal delay of the reflected signals in relation to the direct sound puts forward a requirement for the minimum volume of the room, which is not recommended to be violated. Meanwhile, when designing a room, its dimensions are chosen based on a given capacity, i.e. solve the problem purely economically, which is wrong. Even in a small concert hall, the optimal structure of early reflections can only be obtained with a given height and width of the hall in front of the stage, less than which it is impossible to descend. It is known, for example, that the sound of a symphony orchestra in a hall with a low ceiling is significantly worse than in a hall with a high ceiling.

The results obtained made it possible to develop recommendations regarding the delay time and the size of the hall. It was taken into account that the first delayed signal, as a rule, comes from the ceiling, the second - from the side walls, the third - from the back wall of the hall. Different requirements for the delay time of the initial reflections are explained by the peculiarities of speech and musical sounds and the difference in the acoustic problems being solved.

Sound type
Speech
Music

To achieve good speech intelligibility, the delays must be relatively small. When sounding music, it is necessary to emphasize the melodic beginning; to ensure the unity of sounds, a greater delay time of the initial reflections is necessary. From this follow the recommended dimensions of concert halls: height and width are not less than 9 and 18.5 m, respectively, and not more than (at the portal) 9 and 25 m.

It is possible to increase the height and width of the hall to some extent only at a distance from the portal of the stage (stage), exceeding approximately 1/4 - 1/3 of the total length of the hall: height up to 10.5 m, width up to 30 m. The length of the hall is chosen taking into account the need receive sufficient direct sound energy at the most remote listening positions. Based on this circumstance, it is recommended to choose the length of the hall on the parterre no more than 40 m, and on the balcony - 46 m.

The table provides information about the geometry of some halls, the acoustic qualities of which are considered good (n - the capacity of the hall, lп - the greatest distance of the listener from the stage in the stalls, lb - the same on the balcony, Dt1 - the delay time of the first reflection).


Column Hall of the House of Unions, Moscow
Great Hall of the Moscow Conservatory
Small Hall of the Moscow Conservatory
Hall of the Academic Chapel, St. Petersburg
Concert Hall, Boston
Concert Hall, New York
Concert Hall, Salzburg
Concert Hall, Caracas

Thus, the minimum dimensions of a room for playing music (height and width) are not related to its capacity, but are determined by the necessary structure of the initial reflections. Even if the room is intended for the performance of music in the absence of listeners (sound recording studio, sound broadcasting studio, music recording studio, film studio listening room), its size should be determined only by the sound quality of the music. "Save" on these sizes - significantly degrade the sound quality.

Historical examples. From the religious and spectacular buildings that have survived to our times, it is clear that the basic provisions of the ray theory were known to the ancient builders and that these provisions were strictly observed. The sizes of Greek and Roman open-air theaters were chosen to make the most use of the energy of reflected waves.

The theaters contained three main parts:

A stage (shena) with a depth of 3.5 - 4 m in Greece and 6 - 8 m in Rome, on which a theatrical action was played;
The platform in front of the stage - the orchestra (orhestra literally "place of dancing"), on which the choir was located and the dancers performed;
Audience seats rising in steps around the orchestra, forming the so-called amphitheater (from the Greek words amphi - "on both sides", "around" and theatron - "place of spectacles").

The sounds from the performers reached the audience, located on the amphitheater, directly 1, as well as after reflections from the surface of the orchestra (beam 2) and wall 3, located behind the stage (Fig. 9, a). The plane of the orchestra was covered with a highly reflective material. As Vitruvius pointed out, the height of wall 3 should be chosen equal to the height of parapet 4, which encloses the upper row of the amphitheater, "to improve acoustics." Apparently, it was a question of preventing excessive scattering of sound energy in space. The depth of the stage in Greek theaters was made small so that the beams 5 reflected from the back wall would not be too late in relation to the direct beam 1 and would not impair the intelligibility of the actors' speech. Part of the sound energy, reflected from walls 3 and 4, went up. In modern indoor theater halls, this energy is reflected down the ceiling and increases the intensity of the sound in the audience seats. Dances took place in the orchestra and a choir was located, repeating the actors' replicas, i.e. performing the task of sound amplification. When the choir is located at point 1, the sound rays, reflected from wall 3 (Fig. 9, b), come to the viewer with a large time delay, causing an echo. To reduce this shortcoming in Roman theaters, the choir began to be located closer to the stage, at point 2. Then, to direct energy towards the audience, they began to use reflections from the stage (its height in Roman theaters reached 3.5 m), and the dancers occupied the vacated part of the orchestra. In modern theaters, musicians are in front of the stage, and the name of the site they occupy has passed to them.

Rice. nine

A special role in amplifying and enriching the sound was played by the so-called "harmonics" - systems of resonators in the form of bronze cylindrical vessels and clay amphorae jugs. They were located in niches in the wall behind the seats and under the benches. The Greeks believed that for the euphony of speech and music, resonators should be selected or tuned according to the tones of musical scales: enharmonic, chromatic and diatonic.

The first system, according to their creators, gave the sounds solemnity and severity;
The second, thanks to the "crowding" notes, is refinement, tenderness to the sound;
The third - due to the consonance of the intervals - the naturalness of the musical performance.

Obviously, during the construction of theaters, ancient architects sought and found technical ways to convey to the audience and listeners not only semantic (semantic), but also artistic (aesthetic) information, and sought to enrich the musical sound.

The theater and concert halls of the 18th and 19th centuries were distinguished by their rational form and wisely chosen sizes. A number of acoustically good theater and concert halls were built in various countries in the 20th century.

Bad decisions. It would seem that the experience accumulated over the millennia should be used by modern architects and builders. Meanwhile, examples of unsatisfactory acoustic solutions are multiplying, for example, the construction of halls with a round or elliptical shape (Coliseum cinema in St. Petersburg, Tchaikovsky concert hall in Moscow, etc.). They form zones of focusing of the reflected rays and zones into which the reflected rays either do not fall or fall with a large time delay. In a hall that is round in plan (Fig. 10 on the right), beam 1 tangent to the wall remains in the zone close to the wall during subsequent reflections. Beams 2, propagating approximately in a diametrical direction, after reflection form a virtual image of the source I ", in which the sound intensity, as in the annular zone near the wall, is increased. Halls with a flat ceiling and a low stage portal are unsatisfactory (Fig. 11, a) The ABC zone turns out to be a kind of trap for a significant part of the energy emitted by the sound source.Only the DE zone gives useful reflections, but they fall only into the remote part of the EC hall.The design with a diffuse ceiling (Fig. 11,b), an acoustic shell and a visor is preferable ( Fig. 11, c).

Figure 11

Acoustically unsatisfactory was the famous Albert Hall in London, 56 m wide and 39 m high. Due to the unusually high height of the hall, the path difference between the direct sound and the sounds reflected from the ceiling reached 60 m, which gave a delay of almost 200 ms. The center of curvature of the concave ceiling was in the area occupied by the listeners, which generated a strong echo.

An example of an unsuccessful acoustic solution is the Great Hall of the Central Theater of the Russian Army (TsTRA). The main disadvantages of the hall are: a large width, equal to 42 m in the middle of the hall, and an excessively high ceiling - at the portal 18 m above the stage tablet (Fig. 12). Reflections from the side walls do not arrive in the central part of the hall, and the first reflections from the ceiling arrive in the middle of the stalls with a delay of more than 35 ms. As a result, speech intelligibility in the stalls is low, despite the closeness of the actors to the audience. The shape of the back wall of the hall and the parapet of the balcony is part of a circle, the center of which is located on the proscenium at point O. The sounds reflected from the back wall and the parapet of the balcony return to the same point and are heard as a strong echo, because the delay exceeds 50 ms. When the actor moves to the AND point, the conjugate foci AND" and AND" are shifted to the ground. As a result, the echo appears in the front rows of the stalls.

Once upon a time, the MTUCI assembly hall was distinguished by good acoustics, where symphony concerts were even held, broadcast on the radio. Acoustic conditions deteriorated significantly after the refurbishment of the hall. The design of the balcony railing was changed, in the depth of which a reflective shield was placed. Strong reflections from the parapet and shield worsened the sound in the stalls. Due to the large delays, speech intelligibility has decreased.

An example of an unsuccessful acoustic solution is the Central Concert Hall of the Rossiya Hotel in Moscow. The square shape of the hall led to a depletion of the natural frequency spectrum, the low ceiling creates a small delay in the first reflections, and the large width of the hall leads to the fact that reflections from the walls do not fall into the first half of the stalls. Three times they tried to improve the sound by replacing sound-absorbing materials and placing them in the hall. However, it was not possible to compensate for the deliberately unsuccessful initial form of the hall.

Rice. 12

Even in rooms with correctly chosen shape and linear dimensions, the proportions of which approach the "golden section", sound flaws are found, the elimination of which takes a lot of time, effort and money. Sound and television broadcasting studios need careful preparation for normal operation. An example is the set of works on the preparation of studio N5 of the State House of Radio Broadcasting and Sound Recording (GDRZ). The studio is intended for the performance of works of large forms with the participation of a symphony orchestra and choir in the presence of listeners. Its linear dimensions (29.8 x 20.5 x 14 m) almost correspond to the "golden section", the estimated reverberation time at medium frequencies is 2.3 s. Due to the large height and width, the arrival time of the initial reflections is not optimal. To reduce the length of the paths of the reflected rays, reflective panels were fixed above the location of the orchestra and on the side walls. It took several times to change the position of the panels and reduce the area of sound-absorbing structures before the musicians and sound engineers recognized the sound quality as good. This example shows how subtle and meticulous the acoustical setting of the rooms is.

There are halls designed for a small number of listeners, respectively, a small area and low. Their authors, apparently, believed that with the small size of the hall, "everything will be heard well." In reality, in such halls, a dense structure of initial reflections is formed at the listening positions. Because of this, with a short reverberation time, the sound turns out to be "flat", similar to the sound in the open air, and with a long reverberation time, the "transparency" of the sound is lost, and the masking of subsequent musical sounds by the previous ones begins.

Also unsatisfactory for the most part are the so-called assembly halls. They are intended for meetings, i.e. to sound speech. Low ceiling, smooth parallel walls, devoid of acoustic finishes give rise to suboptimal initial reflections. Attempts to hold concerts in them do not bring success. Music sounds bad. Worst of all, concerts in such halls spoil the audience. The acoustics of the so-called "concert-sports" halls are below any criticism.

In our country, the "struggle against architectural excesses" has brought great harm to the quality of theater and concert halls. All sound-scattering and sound-absorbing structures and even upholstered seats, designed to serve as the equivalent of absent spectators, were declared "excesses". As a result, the listening positions have a poor structure of initial reflections, low diffuseness, and with partial filling - excessive "boom".

The best halls. The Column Hall of the House of the Unions, the Great and Small Halls of the Moscow Conservatory, the Great Hall of the St. Petersburg Philharmonic and some other halls of the old building remain unsurpassed in sound quality.

The achievements of domestic architectural acoustics include the auditoriums of the Children's Musical Theater, the Theater. Evg. Vakhtangov, Moscow Drama Theatre. A.S. Pushkin, the ZiL Palace of Culture, the studios of the State Recording House, the sound recording studio and the Mosfilm listening room. During their design and construction, the provisions and recommendations of domestic and foreign acousticians were taken into account.

In these halls, the requirements of geometric acoustics are met: the shape and dimensions are rationally chosen, which ensured a high degree of field diffuseness and optimization of the delay times of initial reflections. In each specific case, their architectural and planning solutions are chosen. The halls of relatively small width are given the shape of a rectangular parallelepiped. Such are the Great and Small Halls of the Moscow Conservatory, the Great Hall of the Moscow House of Scientists. With a small width, the number of reflections arriving at the listener's seats increases rapidly with time and in the final part of the reverberation process is so large that it provides good diffuseness of the field. In the halls of large width (Columned Hall of the House of the Unions, the Great Hall of the St. Petersburg Philharmonic), sound-diffusing structures were introduced in the form of a row of columns. In modern large-capacity halls, good sound dispersion is achieved by dividing walls and ceilings and installing large scattering surfaces on the walls.

The material with which the walls and ceiling are finished is important. Wood is the best. The sound of music in the halls decorated with wood is distinguished by a beautiful timbre coloring. On the contrary, reinforced concrete structures, especially thin ones, and plaster on a chain-link mesh are completely contraindicated. Sounds reflected from these surfaces have an unpleasant "metallic" tint.

Conclusion

The three considered theories from different angles explain the acoustic processes occurring in the premises. Of these, only one - statistical - allows you to determine a numerically important value that characterizes the acoustic properties of the room - the reverberation time. One should only consciously, critically treat the resulting numerical assessment, understand that in most cases, especially when considering large premises, it is indicative.

According to modern views, it is customary to divide the process of echo, reverberation into two parts: initial, relatively rare delayed pulses, and a sequence of pulses that is more compacted in time. The first part of the echo is evaluated from the standpoint of geometric (ray) theory, the second - from the standpoint of statistical theory.

Geometric theory is more applicable to the analysis of acoustic processes in large rooms - concert and theater halls, large studios. The optimal dimensions of the hall (studio) are determined based on the analysis of the initial reflections. When designing large rooms, the calculation of the reverberation time can give a result that differs significantly from the real one, and most importantly, this value does not allow you to fully evaluate the acoustic quality of the room. In such an estimate, the initial reflections play the main role. The correct timing of the initial reflections ensures high sound quality even when the reverb time is not optimal.

Statistical and wave theories are especially applicable to relatively small rooms, such as sound broadcasting studios and auditoriums for various purposes. The results of these theories seem to complement each other. The first makes it possible to estimate the reverberation time, the second - to calculate the spectrum of natural (resonant) frequencies, adjust the dimensions of the room so that the spectrum of natural frequencies in the low frequency region is more uniform.

It would be very interesting and important to combine the provisions of acoustic theories, to create a unified theory that explains from a general position the complex acoustic processes that occur in rooms of different purposes, different shapes and sizes. But until this is achieved, it remains to consciously use existing theories and achieve the best solutions with their help.

Literature

Acoustics: Handbook / ed. M.A. Sapozhkov. - M.: Radio and communication, 1989.
Brekhovskikh L.M. Propagation of waves in layered media. - M.-L.: Ed. Academy of Sciences of the USSR, 1958.
Dreyzen I.G. Course of electroacoustics, part 1. - M .: Svyazradioizdat, 1938.
Dreyzen I.G. Electroacoustics and sound broadcasting. - M.: Svyazizdat, 1951.
Emelyanov E.D. Sound systems for theaters and concert halls. - M.: Art, 1989.
Kontyuri L. Acoustics in construction. - M.: Stroyizdat, I960.
Makrinenko L.I. Acoustics of public premises. - M.: Stroyizdat, 1986.
Morse F. Oscillations and sound. - M.-L.: Gostekhizdat, 1949.
Sapozhkov M.A. Soundproofing of premises. - M.: Communication, 1979.
Skuchik E. Fundamentals of acoustics. - M.: Ed. foreign lit., 1959.
Strutt J.W. (Lord Rayleigh). Theory of sound. - M.: GITTL, 1955.
Furduev V.V. Electroacoustics. - M.-L.: OGIZ-GITTL. 1948.
Furduev V.V. Acoustic fundamentals of broadcasting. - M.: Svyazizdat, 1960.
Furduev V.V. Modeling in architectural acoustics // Technique of cinema and television, 1966. N 10

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During the lesson, everyone will be able to get an idea of \u200b\u200bthe topic “Reflection of waves. Sound Resonance. In this lesson, we will explore such an interesting phenomenon of wave reflection as an echo, and calculate the conditions necessary for its occurrence. We will also conduct a fascinating experience with a musical tuning fork in order to better understand what sound resonance is.

So, we are completing Chapter 7 - "Oscillations and Waves" - with interesting phenomena. This is the reflection of waves and sound resonance. You know that in an empty room, in the mountains or under the vaults of a building of some kind of arch, you can observe a wonderful phenomenon - an echo. What is an echo? Echo- This is the phenomenon of reflection of sound waves from dense objects. When can a person hear an echo? It turns out that for a person to be able to distinguish (his hearing aid was able to distinguish between two signals), it is necessary that the time delay be 0.06 s. Let's calculate: the wave propagation speed is 340 m/s in the air, so you can calculate the distance to the object from which the wave will be reflected. It should be clear: when multiplying the speed by this value, the delay, we get 20.4 m. L=V. ∆t = 340 m/s 0.06 m/s = 20.4 m.

But, you understand that reflection is the movement of a wave in one direction, then it undergoes reflection in the other, so the distance that we received can be safely divided in half and put a person at a distance from the barrier from which the sound will be reflected, and then you can echo hear. You also need a well reflective surface, because if, for example, the room is large enough, it is crowded with a lot of furniture (upholstered furniture) and people, then all these objects absorb the sound wave, so the echo is indistinguishable. There is simply not enough energy for a sound wave to have this phenomenon. Where is this phenomenon used? Of course, it's entertaining to listen to the echo in the mountains, it's great to sing under musical arches, which are often used in the architecture of the 19th century, but there are real devices that use this property. For example, a speaker. If I now fold my hands like this, you immediately heard that my sound became more powerful, although the people who would stand at my side, the sound from my vocal cords would be much quieter. Therefore, an interesting phenomenon occurs: the walls of the horn amplify the sound wave, increasing the signal power. What is an echo sounder? This is a compound word derived from two words: "echo" - "reflection", "lot" - a device that measures the depth of a reservoir. A lot is a simple stone on a fisherman's rope. The echo sounder for people who sail on large ships is arranged as follows. Under the side of the ship is a receiver and a source of sound waves. A sound wave travels from the source of the sound wave, reaches the bottom, is reflected and enters the receiver of the sound waves. The time is fixed, which passes between the signal and its arrival back. ∆t = 0.06 s. And the distance, which is obtained by such a calculation, is divided in half, and we find the depth of the reservoir. Echo sounders are used not only at sound frequencies, but also at infrasound or ultrasound. We discussed in the last paragraph how it is used. The principle is the same. The phenomenon of reflection of sound waves is used. Let's look at another interesting sound phenomenon - this sound resonance. Let me remind you: this is the phenomenon of an increase in the amplitude of forced oscillations, while observing the frequency of natural oscillations of the system and forced ones. I remind you: any system that can oscillate has its own frequency. This frequency is formed by the very design of the device, which can oscillate. If we make this device oscillate with an external force that has just such a frequency of forced oscillations n 0 = n VIN, there will be an increase in sound vibrations, because an increase in amplitude entails an increase in sound, energy power. To explain this phenomenon in detail so that you understand what it means resonance , we will work with such a special device that is used in music. This device is called a tuning fork. The fork is made of steel and has a natural frequency corresponding to the note la in this experiment. A special resonator box was selected for this tuning fork, by trial and error, by mathematical calculations. What kind of box is this? What he does with the sound, we will now see in practice. Before us is a tuning fork. I have a rubber hammer with which we will cause vibrations. This tuning fork will have forced vibrations. First, in order to understand what the resonator box is for, I will try to cover the resonator box with a simple sheet of paper like this. Listen carefully to what will happen to the sound itself. If you notice something, let's repeat the experience again. I will try to cause a more serious oscillation by increasing the energy in the system. So, the resonator box increases the amplitude of the resulting oscillations. How he does it? It redistributes the energy that I put into the system. This means that the tuning fork in the resonator box causes the very soundboard of the box and the air that is inside this box to vibrate. The vibrations add up and amplify the sound. At the same time, the law of conservation of energy is fulfilled in our country, i.e. with a resonator box, the tuning fork sounds less in time, but stronger. Let's continue the experiment. Let's see how we can stop this sound vibration. I touched the legs of the tuning fork, and the attenuation coefficient of this system became very large, the oscillation stopped almost instantly. Again, no hesitation. Now we will see the phenomenon of resonance, what happens if I take exactly the same, having exactly the same sound frequency, another tuning fork. Look, the resonator boxes will be directed at each other so that the air gap is insignificant and so that the vibrations do not fade, and the effect is maximum. So, I cause oscillations in this tuning fork. The sound wave propagates, goes into space, and if the frequency is exactly the same for the tuning fork, then resonance should occur. Let's see, I can hear the second tuning fork. Let's repeat it again: the tuning fork is sounding, it has stopped sounding. Let's check, maybe I have a special tuning fork on the left. Let's try to cause oscillation in the second tuning fork and listen to what will happen with the first. There is fluctuation. So, the resonance condition is fulfilled: the frequencies coincide, the amplitude increases. The system responds selectively to external fluctuations. Selects only the frequency to which it is tuned. Let's check this, if I now change the frequency of oscillation of one of the tuning forks (I just screw the clutch here), the body that oscillates will change in mass, and its frequency will change. Therefore, there will be no resonance. I am sure of this, let's check by experience whether this is really so. There is no resonance, and therefore there was no sound either. Let's see, if I do it in reverse order, if this tuning fork sounds, then maybe I'm deceiving you, we'll see. There was no resonance.

So, today we have studied important sound phenomena. This is the reflection of sound waves and the phenomenon of sound resonance. Thank you for your attention.

Sound propagates from the sounding body evenly in all directions, if there are no obstacles in its path. But not every obstacle can limit its spread. Sound cannot be shielded from a small sheet of cardboard, as from a beam of light. Sound waves, like any waves, are able to go around obstacles, "not notice" them if their dimensions are smaller than the wavelength. The length of sound waves heard in the air ranges from 15 m to 0.015 m. If the obstacles in their path are smaller (for example, tree trunks in light forests), then the waves simply go 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.

The way sound moves from one medium to another. This phenomenon is quite complex, but it obeys the 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 boundary of these media, it is almost completely reflected. A very small part of its energy is spent on the vibration of the surface layers of another medium. 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 not hear anything. Fish do not hear the sound that is heard above the surface of the sea, but the sound from the body vibrating in the water, they hear well.

Sound is heard through thin walls because it makes them vibrate, and they seem to reproduce the sound already in another room. Good soundproofing materials - wool, fleecy carpets, walls made of foam concrete or porous dry plaster - just differ in that they have a lot of interfaces between air and a solid body. Passing through each of these surfaces, the sound is repeatedly reflected. But, in addition, the very medium in which sound propagates absorbs it. The same sound is heard better and farther 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 sounds, less - low, such as bass. That is why the ship's whistle emits such a low sound (its frequency is not more than 50 Hz): a low sound is heard at a greater distance. The big bell in the Moscow Kremlin, when it was still hanging on the bell tower "Ivan the Great", was heard for 30 miles - it hummed in a tone of about 30 Hz (fa suboctave). Infrasounds are absorbed even less, especially in water. Fish hear them for tens and hundreds of kilometers. 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 a sound of 10 kHz is attenuated by half at 2200 m.

Sound wave energy

The chaotic motion 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 - vibrational. The energy for such movement is given to the air particles by a vibrating body (sound source); while it oscillates, energy is continuously transferred from it to the surrounding air. The further the sound wave passes, the weaker it becomes, the less energy it has. The same thing happens with a sound wave in any other elastic medium - in a liquid, in a metal.

The sound propagates evenly in all directions, and at each moment the layers of compressed air that have arisen 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 an ever larger and larger surface of the "ball". The surface of the ball is proportional to the square of the radius, so 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. Therefore, the sound becomes weaker at a distance. The Russian scientist N. A. Umov introduced the concept of energy density flux into science. It is also convenient to measure the strength (intensity) of sound by the magnitude of the energy flow. 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 flow of energy density, the greater the strength of the sound. The energy flow is measured in watts per square meter (W/m²).

SOUND REFLECTION- a phenomenon that occurs when a sound wave falls on the interface between two elastic media and consists in the formation of waves propagating from the interface into the same medium from which the incident wave came. As a rule, O. z. accompanied by the formation of refracted waves in the second medium. A special case of O. z. - reflection from a free surface. Reflection at flat interfaces is usually considered, but one can speak of O. z. from obstacles of arbitrary shape, if the size of the obstacle is much larger than the length of the sound wave. Otherwise, there is sound scattering or sound diffraction.
The incident wave causes the boundary between the media to move, as a result of which reflected and refracted waves arise. Their structure and intensity should be such that, on both sides of the interface, the particle velocities and elastic stresses acting on the interface are equal. The boundary conditions on the free surface consist in the equality to zero of the elastic stresses acting on this surface.
The reflected waves may have the same type of polarization as the incident wave, or they may have other polarizations. In the latter case, one speaks of a transformation, or conversion, of a mode upon reflection or refraction. There is no conversion only when a sound wave propagating in a liquid is reflected, since only longitudinal waves exist in a liquid medium. When a sound wave passes through the interface between solids, as a rule, both longitudinal and transverse reflected and refracted waves are formed. The complex nature of O. z. takes place at the crystalline boundary. media, where in the general case there are reflected and refracted waves of three decomp. polarizations.
Reflection of plane waves. The reflection of plane waves plays a special role, since plane waves, being reflected and refracted, remain plane, and the reflection of waves of 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. branches that exist 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 plane interface.

From here follow the laws of reflection and refraction, according to the Crimea: 1) the wave vectors of the incident k i reflected k 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 phase velocities c i, and the corresponding waves are equal to each other:
(subscripts and denote polarizations of reflected and refracted waves). In isotropic media, where the directions of the wave vectors coincide with the directions of the 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 the wave normals; how the 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 the speed for to-l. refracted wave more speed c i incident wave, then for angles of incidence, large so-called. critical angle \u003d arcsin, the normal component of the wave vector of the corresponding refracted wave becomes imaginary, and the transmitted wave itself turns into an inhomogeneous wave running along the interface and exponentially decreasing deep into the medium 2 . However, the incidence of a wave on the interface at an angle larger than the critical one may not lead to total reflection, since the energy of the incident radiation can penetrate into the second 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 phase velocity of the wave resulting from the conversion is greater than the velocity c i falling wave. For angles of incidence, smaller critical. angle, part of the incident energy is carried away from the boundary in the form of a reflected wave with polarization; at , such a wave turns out to be inhomogeneous, damping deep into the medium 1, and does not take part in the energy transfer from the interface. For example, critical angle = arcsin( c t /c L) occurs upon reflection of the transverse acoustic. waves T from the boundary of an isotropic solid body and its conversion into a longitudinal wave L (with t and C L are the velocities of the transverse and longitudinal sound waves, respectively).
The amplitudes of the reflected and refracted waves, in accordance with the boundary conditions, are linearly expressed in terms of the amplitude A i incident wave, just as these quantities in optics are expressed in terms of the amplitude of the incident e-magn. waves with 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: = Amplitude coefficient. reflections are generally complex: their moduli determine the ratios abs. the amplitudes, and the phases define the phase shifts of the reflected waves. The amplitude coefficients are determined in a similar way. passing The redistribution of the energy of the incident radiation between the reflected and refracted waves is characterized by the coefficient. reflection and transmission in intensity, which are the ratios of the components of the time-averaged energy flux densities normal to the interface in the reflected (refracted) and incident waves:

where are the sound intensities in the corresponding waves, and are the densities of the media in contact. The balance of energy supplied to the interface and carried away from it reduces to the balance of the normal components of the energy fluxes:

Coef. reflections depend both on the acoustic properties of the media in contact, and on the angle of incidence. The nature of the angle dependence is determined by the presence of critical. angles, as well as angles of zero reflection, when falling under which a reflected wave with polarization is not formed.

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

where and c 1,2 - density and speed of sound in adjacent media 1 and 2 . If the speed of sound for the incident wave is greater than the speed of sound for the refracted ( with 1 >c 2), then the critical corner is missing. Coef. reflection is real and varies smoothly from the value

at normal incidence of the wave on the interface up to the value R=- 1 for grazing incidence If acous. impedance r 2 s 2 medium 2 more medium impedance 1 , then at the angle of incidence

coefficient reflection vanishes and all incident radiation 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 сдвиг между падающей и отражённой волнами отсутствует. Величина коэф. отражения меняется от значения R0 with a normal fall to R= 1 at an angle of incidence equal to the critical one. Zero reflection can also take place in this case, if for the acoustic media impedances, the inverse inequality holds the angle of zero reflection is still determined by expression (6). For angles of incidence greater than critical, there is a complete internal. reflection: and incident radiation deep into the medium 2 does not penetrate. In the environment 2 , however, an inhomogeneous wave is formed; the complexity of the coefficients is associated with its occurrence. reflections and the corresponding phase shift between the reflected and incident waves. This shift is explained by the fact that the field of the reflected wave is formed as a result of the interference of two fields: a specularly reflected wave and a wave re-radiated into the medium 1 an inhomogeneous wave that has arisen in a medium 2 . When non-plane (for example, spherical) waves are reflected, such a reradiated wave is actually observed in the experiment in the form of the so-called. side wave (see Waves, section Reflection and refraction of waves).

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

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

When > coefficient. reflection becomes complex, since an inhomogeneous wave is formed in a solid near the boundary. At angles of incidence between the critical angles and part of the incident radiation penetrates deep into the solid in the form of a refracted transverse wave. Therefore, for<<величина лишь при поперечная волна не образуется и |R|= 1. The participation of an inhomogeneous longitudinal wave in the formation of reflected radiation causes, as on the boundary of two liquids, a phase shift of the reflected wave. When > there is a complete ext. reflection: 1. In a solid body near the boundary, only inhomogeneous waves exponentially falling into the depth of the body are formed. The phase shift of the reflected wave for the angles is associated mainly with the excitation at the interface of the leaky Rayleigh waves. Such a wave arises at the boundary of a solid body with a liquid at angles of incidence close to the Rayleigh angle = arcsin ( s/s R), where C R is the Rayleigh wave velocity on the solid surface. Propagating along the interface, the leaky wave is completely re-emitted into the liquid.
If a with > with t, then the total internal there is no reflection at the boundary of a liquid with a solid: the incident radiation penetrates the solid at any angle of incidence, at least in the form of a transverse wave. Total reflection occurs when a sound wave falls under the critical. angle or grazing incidence. For c>c L coefficient. reflections are real, since inhomogeneous waves are not formed at the interface.
Oz propagating in a solid body. When sound propagates in an isotropic solid, max. a 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 upon reflection or refraction of such waves. When falling on a free boundary or an 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 is formed with a polarization that is also parallel to the interface.
When a transverse wave polarized in the plane of incidence is incident on the free surface of a body, both a reflected transverse wave of the same polarization and a longitudinal wave arise at the boundary. At angles of incidence smaller than the critical angle = = arcsin ( cT/cL), coefficient reflections R T and R L- purely real: the reflected waves leave the boundary exactly in phase (or in antiphase) with the incident wave. At > only a specularly reflected transverse wave leaves the boundary; an inhomogeneous longitudinal wave is formed near the free surface.
Coef. reflection becomes complex, and a phase shift occurs between the reflected and incident waves, the magnitude of which depends on the angle of incidence. When a longitudinal wave is reflected from the free surface of a solid body at any angle of incidence, both a reflected longitudinal wave and a transverse wave polarized in the plane of incidence arise.
If the boundary of a solid body is in contact with a liquid, then when waves (longitudinal or transverse, polarized in the plane of incidence) are reflected in the liquid, an additional refracted longitudinal wave appears. At the interface between two isotropic solid media, this system of reflected and refracted waves is supplemented by a refracted transverse wave in the medium 2 . Its polarization also lies in the plane of incidence.

O. h. at the interface between anisotropic media. O. h. at the crystalline interface. environment is complex. The velocities of both the reflected and refracted waves in this case are themselves functions of the angles of reflection and refraction (see Fig. Crystal acoustics;) therefore, even the definition of angles from a given angle of incidence faces serious problems. difficulties. If the 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 on a perpendicular NN" drawn to the interface through the end of the wave vector k i incident wave, at the points where this perpendicular intersects dec. cavity surfaces of wave vectors (Fig. 3). The number of reflected (or refracted) waves actually propagating from the interface into the depth of the corresponding medium is determined by how many cavities the perpendicular intersects NN". If the intersection with to-l. 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 in several. points (points a 1 and a 2 in fig. 3). Of the possible positions of the wave vector k r (or k t) really observed waves correspond only to those for which the radial velocity vector, coinciding in direction with the external. normal to the surface of the wave vectors, is directed from the boundary into the depth of the corresponding medium.

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, fast and slow quasi-transverse waves, respectively.

As a rule, reflected (refracted) waves belong to dec. acoustic branches. fluctuations. However, in crystals with 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 oscillation branch.
Experimentally, finite beams of sound waves are observed, the propagation directions of which are determined by the radial velocities. The directions of rays in crystals differ significantly from the direction of the corresponding wave vectors. The radial velocities of the incident, reflected and refracted waves lie in the same plane only in exceptional cases, for example. when the plane of incidence is the plane of symmetry for both crystals. avg. In the general case, the reflected and refracted rays occupy various positions both in relation to each other and in relation to the incident ray and the normal. NN" to the boundary. In particular, the reflected beam can lie in the plane of incidence on the same side of the normal N, which is the incident beam. The limiting case of this possibility is the superimposition of the reflected beam on the incident beam at an oblique incidence of the latter.

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

Influence of attenuation on the nature of O. z. . Coef. reflections and transmissions do not depend on the sound frequency 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 also distorts its dependence on the angle of incidence, especially near the critical. corners (Fig. 5, a). When reflected from the interface between a liquid and a solid, the damping 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 damping at such angles of incidence, total internal reflection takes place and | 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 | R| (curves 2 - 4) . As the frequency increases and the corresponding increase in the coefficient. damping, the depth of the minimum increases until, finally, at a certain frequency f 0 , called zero reflection frequency, min. value | R| does not vanish (curve 3 , rice. 5, b). A further increase in frequency leads to a broadening of the minimum (curve 4 ) and to influence of effects of attenuation 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 leaky Rayleigh wave, which is excited by the incident radiation and participates in the formation of the reflected wave. When the sound frequency f equal to the 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; b- angular dependence | R\ near the Rayleigh angle at different values of absorption of transverse waves in steel at a wavelength. Curves 1 - 5 correspond to an increase in this parameter from a value of 3 x 10 -4 (curve 1 ) to the value = 1 (curve 5) due to the corresponding increase in the frequency of the incident ultrasonic radiation.

O. h. from layers and plates. O. h. from the layer or plate is resonant. The reflected and transmitted waves are formed as a result of multiple reflections of waves at the layer boundaries. In the case of a liquid layer, the incident wave penetrates the layer at an angle of refraction 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 layer boundaries (Fig. 6, a). Angle is the angle of refraction corresponding to the angle of incidence at the layer boundary. If the speed of sound in the layer with 2 more speed of sound with 1 in the surrounding fluid, then the system of re-reflected waves arises only when the angle of the total int. reflections \u003d arcsin (c 1 / c 2). However, for sufficiently thin layers, the transmitted wave is also formed at angles of incidence larger than the critical one. In this case, the coefficient reflection from the layer turns out to be abs. value is less than 1. This is due to the fact that at in the layer near the boundary on which the wave is incident from outside, an inhomogeneous wave arises that falls exponentially into the depth of the layer. If the layer thickness d is less than or comparable to the depth of penetration of an inhomogeneous wave, then the latter perturbs the opposite boundary of the layer, as a result of which the transmitted wave is radiated from it into the surrounding liquid. This phenomenon of wave penetration is analogous to the penetration of a particle through a potential barrier 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 - odds. O. h. respectively on the upper and lower boundaries. At is a periodic audio frequency function f and layer thickness d. At when there is penetration of the wave through the layer, | R | with increasing f or d tends monotonically to 1.

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

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

and the waves emerging into the upper medium after two successive reflections will be in antiphase and cancel each other out. On the contrary, all re-reflected waves enter the lower medium with the same phase, and the amplitude of the transmitted wave turns out to be maximum. Under normal wave incidence on the layer, complete transmission takes place when an integer number of half-waves fit into the layer thickness: d= where P= 1,2,3,..., - sound wave length in the layer material; therefore, layers for which condition (8) is satisfied are called half wave Relation (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 reradiates 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 boundary of these liquids when they are directly. contact. In addition to half-wave layers in acoustics, as in optics, the so-called. quarter-wave layers, the thicknesses of which satisfy the condition ( n= 1,2,...). Choosing an appropriate acoustic layer impedance, you can get zero reflection from the wave layer with a given frequency f at a certain angle of incidence on the layer. Such layers are used as antireflection acoustic layers.
For the reflection of a sound wave from an infinite solid plate immersed in a liquid, the character of reflection described above for the liquid layer will be preserved in general terms. In the case of re-reflections in the plate, in addition to the longitudinal ones, shear waves will also be excited. The angles and, under which the longitudinal and transverse waves propagate in the plate, respectively, 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 the liquid layer, a system of alternating maxima and minima. Complete transmission through the plate occurs when the incident radiation excites in it one of the normal waves, which are lamb waves.Resonance character of O. z. from the layer or plate is erased as the difference between them acoustic decreases. properties from the properties of the environment. Acoustic increase. attenuation in the layer also leads to smoothing of dependencies and | R(fd)|.

Reflection of non-planar 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 an arbitrary wavefront can be represented as a set of plane waves with the same circular frequency, but with diff. directions of the wave vector k. Main characteristic of the incident radiation is its spatial spectrum - a set of amplitudes A(k) plane waves collectively forming an incident wave. Abs. the value of k is determined by the frequency, so its components are not independent. When reflected from a plane z= 0 normal component kz is given by tangential components k x , k y: k z =Each plane wave, which is part of the incident radiation, falls on 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 in terms of the spatial spectrum of the incident radiation A(k x , k y) and coeff. reflections R(k x , k y):

Integration extends to the region of arbitrarily large values k x and k y. If the spatial spectrum of the incident radiation contains (as in the reflection of a spherical wave) components with k x(or k y), large, then in the formation of the reflected wave, in addition to waves with real kz non-uniform waves also take part, for which k, is a purely imaginary quantity. This approach, proposed in 1919 by H. Weyl and further developed in the representations of Fourier optics, gives successive results. description of the reflection of an arbitrary wave from a plane interface.
When considering O. z. a ray 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. This takes 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 the so-called. side waves, as well as leaky surface waves (Rayleigh, etc.) or leaky waveguide modes (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 the practice of the reflection is spherical. waves collimated acoustically. 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 O, depends on the ratio between the speeds of sound with 1 and from 2 to contacting liquids I and II (Fig. 7). If c t > c 2 , then the critical the angle is absent and the reflection occurs according to the geom laws. acoustics. In the environment I there is a reflected spherical. wave: reflected rays intersect at a point O". forming a virtual image of the source, and the wavefront of the reflected wave is a part of the sphere centered at the point O".

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

When c2 >cl and there is a critical angle in the medium I in addition to the reflected spherical. waves, another component of the reflected radiation arises. Rays incident on the interface under the critical. angle excite a second wave in the medium, which propagates at a speed with 2 along the interface and is re-emitted into medium I, forming the so-called. side wave. Its front is formed by points, to which, at the same moment of time, the rays that came out of the point reached O along OA and then moved again to Wednesday I in decomp. points of the interface from the point BUT to the point With, in which the front of the refracted wave is located at this moment. In the plane of the drawing, the side wave front is a straight line segment SW, inclined to the boundary at an angle and extending to the point AT, where it merges with the front of the mirror-reflected spherical. waves. In space, the lateral wave front is the surface of a truncated cone that arises during the rotation of the segment SW around a straight line 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 acoustics of the ocean.

Reflection of acoustic beams of finite cross section. Reflection of collimated sound beams, the wave front to-rykh in the main. part of the beam is close to flat, occurs for most angles of incidence as if a plane wave is reflected. When a beam incident from a liquid is reflected onto the interface with a solid body, a reflected beam arises, the shape of which is a mirror reflection of the amplitude distribution in the incident beam. However, at angles of incidence close to the longitudinal critical. corner or Rayleigh angle along with specular reflection occurs eff. excitation of a lateral or leaky Roley wave. The field of the reflected beam in this case is a superposition of the specularly reflected beam and the reradiated waves. Depending on the beam width and the elastic and viscous properties of the adjacent media, either a lateral (parallel) beam shift occurs in the interface plane (the so-called Schoch shift) (Fig. 8) or a significant broadening of the beam and the appearance of a thin

Rice. 8. Lateral displacement of the beam upon reflection: 1 - incident beam; 2 - specularly reflected beam; 3 - real reflected beam.

structures. When the beam is incident at the Rayleigh angle, the nature of the distortion is determined by the ratio between the beam width l and radiats. damping of the leaky Rayleigh wave

where is the length of the sound wave in the liquid, BUT is a numerical factor close to one. If the beam width is much greater than the length of the radii. damping, only the beam shifts along the interface by an amount. In the case of a narrow beam, due to 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 amplitude minimum occurs and the beam splits into two parts. Non-specular reflection of collimes. beams also arise at the boundary of two liquids at angles of incidence close to critical, as well as when beams are reflected from layers or plates.

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

In the latter case, the nonspecular nature of the reflection is due to the excitation of leaky waveguide modes in the layer or plate. An important role is played by lateral and leaky waves in the reflection of focused ultrasonic beams. In particular, these waves are used in acoustic microscopy for the formation of acoustic. images and carrying out quantities, measurements.

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, Moscow, 1989; 4) Сagniard L., Reflexion et refraction des ondes seismiques progressives, P., 1939; 5) Ewing W. M., Jardetzky W. S., Press F., Elastic waves in layered media, N. Y. - , 1957, ch. 3; 6) Au1d B. A., Acoustic fields and waves in solids, v. 1 - 2, N. Y. - , 1973; 7) Vertoni H. L., Tamir T., Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces, "Appl. Phys.", 1973, v. 2, no. 4, p. 157; 8) Mott G., Reflection and refraction coefficients at a fluid-solid interface, "J. Acoust. Soc. Amer.", 1971, v. 50, no. 3 (pt. 2), p. 819; 9) Wesker F. L., Richardson R. L., Influence of material properties on Rayleigh critical-angle reflectivity, "J. Acoust. Soc. Amer.", 1972, v. 51. .V" 5 (pt 2), p. 1609; 10) Fiorito R., Ubera11 H., Resonance theory of acoustic reflection and transmission through a fluid layer, ".I. Acoust. soc. Amer.", 1979, v. 65, no. 1, p. 9; 11) Fiorft o R., Madigosky W., C bera 11 H., Resonance theory of acoustic waves interacting with an elastic plate. "J. Acoust. soc. Amer.", 1979, v. 66, no. 6, p. 1857; 12) Neubauer W. G., Observation of acoustic radiation from plane and curved surfaces, in: Physical acoustics. Principles and methods, ed. by W. P. Mason, R. N. Thurston, v. 10, N. Y. - L., 1973, ch. 2.