Whether sound waves. Why does a sound wave appear? Sound sounding of depths
Sound is sound waves that cause vibrations of tiny particles of air, other gases, and liquid and solid media. Sound can only arise where there is a substance, no matter what state of aggregation it is in. In vacuum conditions, where there is no medium, sound does not propagate, because there are no particles there that act as distributors of sound waves. For example, in space. Sound can be modified, altered, turning into other forms of energy. Thus, sound converted into radio waves or electrical energy can be transmitted over distances and recorded on information media.
sound wave
The movements of objects and bodies almost always cause fluctuations in the environment. It doesn't matter whether it's water or air. During this process, the particles of the medium to which the vibrations of the body are transmitted also begin to vibrate. Sound waves arise. Moreover, movements are carried out in forward and backward directions, progressively replacing each other. Therefore, the sound wave is longitudinal. There is never any lateral movement up and down in it.
Characteristics of sound waves
Like any physical phenomenon, they have their own quantities, with the help of which properties can be described. The main characteristics of a sound wave are its frequency and amplitude. The first value shows how many waves are formed per second. The second determines the strength of the wave. Low-frequency sounds have low frequency values, and vice versa. The frequency of sound is measured in Hertz, and if it exceeds 20,000 Hz, then ultrasound occurs. There are plenty of examples of low-frequency and high-frequency sounds in nature and the world around us. The chirping of a nightingale, the rumble of thunder, the roar of a mountain river and others are all different sound frequencies. The amplitude of the wave directly depends on how loud the sound is. The volume, in turn, decreases with distance from the sound source. Accordingly, the further the wave is from the epicenter, the smaller the amplitude. In other words, the amplitude of a sound wave decreases with distance from the sound source.
Speed of sound
This indicator of a sound wave is directly dependent on the nature of the medium in which it propagates. Both humidity and air temperature play a significant role here. In average weather conditions, the speed of sound is approximately 340 meters per second. In physics, there is such a thing as supersonic speed, which is always greater than the speed of sound. This is the speed at which sound waves travel when an aircraft moves. The plane moves at supersonic speed and even outruns the sound waves it creates. Due to the pressure gradually increasing behind the aircraft, a shock wave of sound is formed. The unit of measurement for this speed is interesting and few people know it. It's called Mach. Mach 1 is equal to the speed of sound. If a wave travels at Mach 2, then it travels twice as fast as the speed of sound.
Noises
There is constant noise in human daily life. The noise level is measured in decibels. The movement of cars, the wind, the rustling of leaves, the interweaving of people's voices and other sound noises are our daily companions. But the human auditory analyzer has the ability to get used to such noise. However, there are also phenomena that even the adaptive abilities of the human ear cannot cope with. For example, noise exceeding 120 dB can cause pain. The loudest animal is the blue whale. When it makes sounds, it can be heard over 800 kilometers away.
Echo
How does an echo occur? Everything is very simple here. A sound wave has the ability to be reflected from different surfaces: from water, from a rock, from walls in an empty room. This wave returns to us, so we hear secondary sound. It is not as clear as the original one, since some of the energy of the sound wave is dissipated when traveling to the obstacle.
Echolocation
Sound reflection is used for various practical purposes. For example, echolocation. It is based on the fact that with the help of ultrasonic waves it is possible to determine the distance to the object from which these waves are reflected. Calculations are made by measuring the time it takes for ultrasound to travel to a location and return. Many animals have the ability to echolocation. For example, bats and dolphins use it to search for food. Echolocation has found another application in medicine. During ultrasound examinations, a picture of a person’s internal organs is formed. The basis of this method is that ultrasound, entering a medium other than air, returns back, thus forming an image.
Sound waves in music
Why do musical instruments make certain sounds? Guitar strumming, piano strumming, low tones of drums and trumpets, the charming thin voice of a flute. All these and many other sounds arise due to air vibrations or, in other words, due to the appearance of sound waves. But why is the sound of musical instruments so diverse? It turns out that this depends on several factors. The first is the shape of the tool, the second is the material from which it is made.
Let's look at this using string instruments as an example. They become a source of sound when the strings are touched. As a result, they begin to vibrate and send different sounds into the environment. The low sound of any stringed instrument is due to the greater thickness and length of the string, as well as the weakness of its tension. And vice versa, the more tightly the string is stretched, the thinner and shorter it is, the higher the sound obtained as a result of playing.
Microphone action
It is based on the conversion of sound wave energy into electrical energy. In this case, the current strength and the nature of the sound are directly dependent. Inside any microphone there is a thin plate made of metal. When exposed to sound, it begins to perform oscillatory movements. The spiral to which the plate is connected also vibrates, resulting in an electric current. Why does he appear? This is because the microphone also has built-in magnets. When the spiral oscillates between its poles, an electric current is generated, which goes along the spiral and then to a sound column (loudspeaker) or to equipment for recording on an information medium (cassette, disk, computer). By the way, the microphone in the phone has a similar structure. But how do microphones work on landlines and mobile phones? The initial phase is the same for them - the sound of the human voice transmits its vibrations to the microphone plate, then everything follows the scenario described above: a spiral, which, when moving, closes two poles, a current is created. What's next? With a landline telephone, everything is more or less clear - just like in a microphone, the sound, converted into electric current, runs through the wires. But what about a cell phone or, for example, a walkie-talkie? In these cases, the sound is converted into radio wave energy and hits the satellite. That's all.
Resonance phenomenon
Sometimes conditions are created when the amplitude of vibrations of the physical body increases sharply. This occurs due to the convergence of the values of the frequency of forced oscillations and the natural frequency of oscillations of the object (body). Resonance can be both beneficial and harmful. For example, to get a car out of a hole, it is started and pushed back and forth in order to cause resonance and give the car inertia. But there have also been cases of negative consequences of resonance. For example, in St. Petersburg, about a hundred years ago, a bridge collapsed under soldiers marching in unison.
This lesson covers the topic "Sound Waves". In this lesson we will continue to study acoustics. First, let's repeat the definition of sound waves, then consider their frequency ranges and get acquainted with the concept of ultrasonic and infrasonic waves. We will also discuss the properties of sound waves in different media and learn what characteristics they have. .
Sound waves – these are mechanical vibrations that, spreading and interacting with the organ of hearing, are perceived by a person (Fig. 1).
Rice. 1. Sound wave
The branch of physics that deals with these waves is called acoustics. The profession of people who are popularly called “hearers” is acousticians. A sound wave is a wave propagating in an elastic medium, it is a longitudinal wave, and when it propagates in an elastic medium, compression and discharge alternate. It is transmitted over time over a distance (Fig. 2).
Rice. 2. Sound wave propagation
Sound waves include vibrations that occur with a frequency from 20 to 20,000 Hz. For these frequencies the corresponding wavelengths are 17 m (for 20 Hz) and 17 mm (for 20,000 Hz). This range will be called audible sound. These wavelengths are given for air, the speed of sound in which is equal to .
There are also ranges that acousticians deal with - infrasonic and ultrasonic. Infrasonic are those that have a frequency of less than 20 Hz. And ultrasonic ones are those that have a frequency greater than 20,000 Hz (Fig. 3).
Rice. 3. Sound wave ranges
Every educated person should be familiar with the frequency range of sound waves and know that if he goes for an ultrasound, the picture on the computer screen will be constructed with a frequency of more than 20,000 Hz.
Ultrasound – These are mechanical waves similar to sound waves, but with a frequency ranging from 20 kHz to a billion hertz.
Waves with a frequency of more than a billion hertz are called hypersound.
Ultrasound is used to detect defects in cast parts. A stream of short ultrasonic signals is directed to the part being examined. In those places where there are no defects, the signals pass through the part without being registered by the receiver.
If there is a crack, an air cavity or other inhomogeneity in the part, then the ultrasonic signal is reflected from it and, returning, enters the receiver. This method is called ultrasonic flaw detection.
Other examples of ultrasound applications are ultrasound machines, ultrasound machines, ultrasound therapy.
Infrasound – mechanical waves similar to sound waves, but having a frequency of less than 20 Hz. They are not perceived by the human ear.
Natural sources of infrasound waves are storms, tsunamis, earthquakes, hurricanes, volcanic eruptions, and thunderstorms.
Infrasound is also an important wave that is used to vibrate the surface (for example, to destroy some large objects). We launch infrasound into the soil - and the soil breaks up. Where is this used? For example, in diamond mines, where they take ore that contains diamond components and crush it into small particles to find these diamond inclusions (Fig. 4).
Rice. 4. Application of infrasound
The speed of sound depends on environmental conditions and temperature (Fig. 5).
Rice. 5. Speed of sound wave propagation in various media
Please note: in air the speed of sound at is equal to , and at , the speed increases by . If you are a researcher, then this knowledge may be useful to you. You may even come up with some kind of temperature sensor that will record temperature differences by changing the speed of sound in the medium. We already know that the denser the medium, the more serious the interaction between the particles of the medium, the faster the wave propagates. In the last paragraph we discussed this using the example of dry air and moist air. For water, the speed of sound propagation is . If you create a sound wave (knock on a tuning fork), then the speed of its propagation in water will be 4 times greater than in air. By water, information will reach 4 times faster than by air. And in steel it’s even faster: 
(Fig. 6).
Rice. 6. Sound wave propagation speed
You know from the epics that Ilya Muromets used (and all the heroes and ordinary Russian people and boys from Gaidar’s RVS) used a very interesting method of detecting an object that is approaching, but is still far away. The sound it makes when moving is not yet audible. Ilya Muromets, with his ear to the ground, can hear her. Why? Because sound is transmitted over solid ground at a higher speed, which means it will reach the ear of Ilya Muromets faster, and he will be able to prepare to meet the enemy.
The most interesting sound waves are musical sounds and noises. What objects can create sound waves? If we take a wave source and an elastic medium, if we make the sound source vibrate harmoniously, then we will have a wonderful sound wave, which will be called musical sound. These sources of sound waves can be, for example, the strings of a guitar or piano. This may be a sound wave that is created in the air gap of a pipe (organ or pipe). From music lessons you know the notes: do, re, mi, fa, sol, la, si. In acoustics, they are called tones (Fig. 7).
Rice. 7. Musical tones
All objects that can produce tones will have features. How are they different? They differ in wavelength and frequency. If these sound waves are not created by harmoniously sounding bodies or are not connected into some kind of common orchestral piece, then such a quantity of sounds will be called noise.
Noise– random oscillations of various physical natures, characterized by the complexity of their temporal and spectral structure. The concept of noise is both domestic and physical, they are very similar, and therefore we introduce it as a separate important object of consideration.
Let's move on to quantitative estimates of sound waves. What are the characteristics of musical sound waves? These characteristics apply exclusively to harmonic sound vibrations. So, sound volume. How is sound volume determined? Let us consider the propagation of a sound wave in time or the oscillations of the source of the sound wave (Fig. 8).
Rice. 8. Sound volume
At the same time, if we did not add a lot of sound to the system (we hit a piano key quietly, for example), then there will be a quiet sound. If we loudly raise our hand high, we cause this sound by hitting the key, we get a loud sound. What does this depend on? A quiet sound has a smaller vibration amplitude than a loud sound.
The next important characteristic of musical sound and any other sound is height. What does the pitch of sound depend on? The height depends on the frequency. We can make the source oscillate frequently, or we can make it oscillate not very quickly (that is, make fewer oscillations per unit time). Let's consider the time sweep of a high and low sound of the same amplitude (Fig. 9).
Rice. 9. Pitch
An interesting conclusion can be drawn. If a person sings in a bass voice, then his sound source (the vocal cords) vibrates several times slower than that of a person who sings soprano. In the second case, the vocal cords vibrate more often, and therefore more often cause pockets of compression and discharge in the propagation of the wave.
There is another interesting characteristic of sound waves that physicists do not study. This timbre. You know and easily distinguish the same piece of music performed on a balalaika or cello. How are these sounds or this performance different? At the beginning of the experiment, we asked people who produce sounds to make them of approximately the same amplitude, so that the volume of the sound is the same. It’s like in the case of an orchestra: if there is no need to highlight any instrument, everyone plays approximately the same, at the same strength. So the timbre of the balalaika and cello is different. If we were to draw the sound that is produced from one instrument from another using diagrams, they would be the same. But you can easily distinguish these instruments by their sound.
Another example of the importance of timbre. Imagine two singers who graduate from the same music university with the same teachers. They studied equally well, with straight A's. For some reason, one becomes an outstanding performer, while the other is dissatisfied with his career all his life. In fact, this is determined solely by their instrument, which causes vocal vibrations in the environment, that is, their voices differ in timbre.
References
- Sokolovich Yu.A., Bogdanova G.S. Physics: a reference book with examples of problem solving. - 2nd edition repartition. - X.: Vesta: publishing house "Ranok", 2005. - 464 p.
- Peryshkin A.V., Gutnik E.M., Physics. 9th grade: textbook for general education. institutions/A.V. Peryshkin, E.M. Gutnik. - 14th ed., stereotype. - M.: Bustard, 2009. - 300 p.
- Internet portal “eduspb.com” ()
- Internet portal “msk.edu.ua” ()
- Internet portal “class-fizika.narod.ru” ()
Homework
- How does sound travel? What could be the source of sound?
- Can sound travel through space?
- Is every wave that reaches a person’s hearing organ perceived by him?
February 18, 2016
The world of home entertainment is quite varied and can include: watching movies on a good home theater system; exciting and exciting gameplay or listening to music. As a rule, everyone finds something of their own in this area, or combines everything at once. But whatever a person’s goals for organizing his leisure time and whatever extreme they go to, all these links are firmly connected by one simple and understandable word - “sound”. Indeed, in all of the above cases, we will be led by the hand by sound. But this question is not so simple and trivial, especially in cases where there is a desire to achieve high-quality sound in a room or any other conditions. To do this, it is not always necessary to buy expensive hi-fi or hi-end components (although it will be very useful), but a good knowledge of physical theory is sufficient, which can eliminate most of the problems that arise for anyone who sets out to obtain high-quality voice acting.
Next, the theory of sound and acoustics will be considered from the point of view of physics. In this case, I will try to make this as accessible as possible to the understanding of any person who, perhaps, is far from knowing physical laws or formulas, but nevertheless passionately dreams of realizing the dream of creating a perfect acoustic system. I do not presume to say that in order to achieve good results in this area at home (or in a car, for example), you need to know these theories thoroughly, but understanding the basics will allow you to avoid many stupid and absurd mistakes, and will also allow you to achieve the maximum sound effect from the system any level.
General theory of sound and musical terminology
What is it sound? This is the sensation that the auditory organ perceives "ear"(the phenomenon itself exists without the participation of the “ear” in the process, but this is easier to understand), which occurs when the eardrum is excited by a sound wave. The ear in this case acts as a “receiver” of sound waves of various frequencies. 
sound wave it is essentially a sequential series of compactions and discharges of the medium (most often the air medium under normal conditions) of various frequencies. The nature of sound waves is oscillatory, caused and produced by the vibration of any body. The emergence and propagation of a classical sound wave is possible in three elastic media: gaseous, liquid and solid. When a sound wave occurs in one of these types of space, some changes inevitably occur in the medium itself, for example, a change in air density or pressure, movement of air mass particles, etc.
Since a sound wave has an oscillatory nature, it has such a characteristic as frequency. Frequency measured in hertz (in honor of the German physicist Heinrich Rudolf Hertz), and denotes the number of oscillations over a period of time equal to one second. Those. for example, a frequency of 20 Hz indicates a cycle of 20 oscillations in one second. The subjective concept of its height also depends on the frequency of the sound. The more sound vibrations occur per second, the “higher” the sound appears. A sound wave also has another important characteristic, which has a name - wavelength. Wavelength It is customary to consider the distance that a sound of a certain frequency travels in a period equal to one second. For example, the wavelength of the lowest sound in the human audible range at 20 Hz is 16.5 meters, and the wavelength of the highest sound at 20,000 Hz is 1.7 centimeters.
The human ear is designed in such a way that it is capable of perceiving waves only in a limited range, approximately 20 Hz - 20,000 Hz (depending on the characteristics of a particular person, some are able to hear a little more, some less). Thus, this does not mean that sounds below or above these frequencies do not exist, but they are simply not perceived by the human ear, going beyond the audible range. Sound above the audible range is called ultrasound, sound below the audible range is called infrasound. Some animals are able to perceive ultra and infra sounds, some even use this range for orientation in space (bats, dolphins). If sound passes through a medium that is not in direct contact with the human hearing organ, then such sound may not be heard or may be greatly weakened subsequently.
In the musical terminology of sound, there are such important designations as octave, tone and overtone of sound. Octave means an interval in which the frequency ratio between sounds is 1 to 2. An octave is usually very distinguishable by ear, while sounds within this interval can be very similar to each other. An octave can also be called a sound that vibrates twice as much as another sound in the same period of time. For example, the frequency of 800 Hz is nothing more than a higher octave of 400 Hz, and the frequency of 400 Hz in turn is the next octave of sound with a frequency of 200 Hz. The octave, in turn, consists of tones and overtones. Variable vibrations in a harmonic sound wave of the same frequency are perceived by the human ear as musical tone. High-frequency vibrations can be interpreted as high-pitched sounds, while low-frequency vibrations can be interpreted as low-pitched sounds. The human ear is capable of clearly distinguishing sounds with a difference of one tone (in the range of up to 4000 Hz). Despite this, music uses an extremely small number of tones. This is explained from considerations of the principle of harmonic consonance; everything is based on the principle of octaves.
Let's consider the theory of musical tones using the example of a string stretched in a certain way. Such a string, depending on the tension force, will be “tuned” to one specific frequency. When this string is exposed to something with one specific force, which causes it to vibrate, one specific tone of sound will be consistently observed, and we will hear the desired tuning frequency. This sound is called the fundamental tone. The frequency of the note “A” of the first octave is officially accepted as the fundamental tone in the musical field, equal to 440 Hz. However, most musical instruments never reproduce pure fundamental tones alone; they are inevitably accompanied by overtones called overtones. Here it is appropriate to recall an important definition of musical acoustics, the concept of sound timbre. Timbre- this is a feature of musical sounds that gives musical instruments and voices their unique, recognizable specificity of sound, even when comparing sounds of the same pitch and volume. The timbre of each musical instrument depends on the distribution of sound energy among overtones at the moment the sound appears.
Overtones form a specific coloring of the fundamental tone, by which we can easily identify and recognize a specific instrument, as well as clearly distinguish its sound from another instrument. There are two types of overtones: harmonic and non-harmonic. Harmonic overtones by definition are multiples of the fundamental frequency. On the contrary, if the overtones are not multiples and noticeably deviate from the values, then they are called non-harmonic. In music, operating with multiple overtones is practically excluded, so the term is reduced to the concept of “overtone,” meaning harmonic. For some instruments, such as the piano, the fundamental tone does not even have time to form; in a short period of time, the sound energy of the overtones increases, and then just as rapidly decreases. Many instruments create what is called a "transition tone" effect, where the energy of certain overtones is highest at a certain point in time, usually at the very beginning, but then changes abruptly and moves on to other overtones. The frequency range of each instrument can be considered separately and is usually limited to the fundamental frequencies that that particular instrument is capable of producing.
In sound theory there is also such a concept as NOISE. Noise- this is any sound that is created by a combination of sources that are inconsistent with each other. Everyone is familiar with the sound of tree leaves swaying by the wind, etc.
What determines the volume of sound? Obviously, such a phenomenon directly depends on the amount of energy transferred by the sound wave. To determine quantitative indicators of loudness, there is a concept - sound intensity. Sound intensity is defined as the flow of energy passing through some area of space (for example, cm2) per unit of time (for example, per second). During normal conversation, the intensity is approximately 9 or 10 W/cm2. The human ear is capable of perceiving sounds over a fairly wide range of sensitivity, while the sensitivity of frequencies is heterogeneous within the sound spectrum. This is how the frequency range 1000 Hz - 4000 Hz, which most widely covers human speech, is best perceived.
Because sounds vary so greatly in intensity, it is more convenient to think of it as a logarithmic quantity and measure it in decibels (after the Scottish scientist Alexander Graham Bell). The lower threshold of hearing sensitivity of the human ear is 0 dB, the upper is 120 dB, also called the “pain threshold”. The upper limit of sensitivity is also perceived by the human ear not in the same way, but depends on the specific frequency. Low-frequency sounds must be much more intense than high-frequency sounds to trigger the pain threshold. For example, the pain threshold at a low frequency of 31.5 Hz occurs at a sound intensity level of 135 dB, when at a frequency of 2000 Hz the sensation of pain will appear at 112 dB. There is also the concept of sound pressure, which actually expands the usual explanation of the propagation of a sound wave in air. Sound pressure- this is a variable excess pressure that arises in an elastic medium as a result of the passage of a sound wave through it.
Wave nature of sound
To better understand the system of sound wave generation, imagine a classic speaker located in a pipe filled with air. If the speaker makes a sharp movement forward, the air in the immediate vicinity of the diffuser is momentarily compressed. The air will then expand, thereby pushing the compressed air region along the pipe. 
This wave movement will subsequently become sound when it reaches the auditory organ and “excites” the eardrum. When a sound wave occurs in a gas, excess pressure and excess density are created and particles move at a constant speed. About sound waves, it is important to remember the fact that the substance does not move along with the sound wave, but only a temporary disturbance of the air masses occurs.
If we imagine a piston suspended in free space on a spring and making repeated movements “back and forth”, then such oscillations will be called harmonic or sinusoidal (if we imagine the wave as a graph, then in this case we will get a pure sinusoid with repeated declines and rises). If we imagine a speaker in a pipe (as in the example described above) performing harmonic oscillations, then at the moment the speaker moves “forward” the well-known effect of air compression is obtained, and when the speaker moves “backwards” the opposite effect of rarefaction occurs. In this case, a wave of alternating compression and rarefaction will propagate through the pipe. The distance along the pipe between adjacent maxima or minima (phases) will be called wavelength. If the particles oscillate parallel to the direction of propagation of the wave, then the wave is called longitudinal. If they oscillate perpendicular to the direction of propagation, then the wave is called transverse. Typically, sound waves in gases and liquids are longitudinal, but in solids waves of both types can occur. Transverse waves in solids arise due to resistance to change in shape. The main difference between these two types of waves is that a transverse wave has the property of polarization (oscillations occur in a certain plane), while a longitudinal wave does not.
Speed of sound
The speed of sound directly depends on the characteristics of the medium in which it propagates. It is determined (dependent) by two properties of the medium: elasticity and density of the material. The speed of sound in solids directly depends on the type of material and its properties. Velocity in gaseous media depends on only one type of deformation of the medium: compression-rarefaction. The change in pressure in a sound wave occurs without heat exchange with surrounding particles and is called adiabatic. 
The speed of sound in a gas depends mainly on temperature - it increases with increasing temperature and decreases with decreasing temperature. Also, the speed of sound in a gaseous medium depends on the size and mass of the gas molecules themselves - the smaller the mass and size of the particles, the greater the “conductivity” of the wave and, accordingly, the greater the speed.
In liquid and solid media, the principle of propagation and the speed of sound are similar to how a wave propagates in air: by compression-discharge. But in these environments, in addition to the same dependence on temperature, the density of the medium and its composition/structure are quite important. The lower the density of the substance, the higher the speed of sound and vice versa. The dependence on the composition of the medium is more complex and is determined in each specific case, taking into account the location and interaction of molecules/atoms.
Speed of sound in air at t, °C 20: 343 m/s
Speed of sound in distilled water at t, °C 20: 1481 m/s
Speed of sound in steel at t, °C 20: 5000 m/s
Standing waves and interference
When a speaker creates sound waves in a confined space, the effect of reflection of the waves from the boundaries inevitably occurs. As a result, this most often occurs interference effect- when two or more sound waves overlap each other. Special cases of the phenomenon of interference are the formation of: 1) Beating waves or 2) Standing waves. Wave beats- this is the case when the addition of waves with similar frequencies and amplitudes occurs. The picture of the occurrence of beats: when two waves of similar frequencies are superimposed on each other. At some point in time, with such an overlap, the amplitude peaks may coincide “in phase,” and the declines may also coincide in “antiphase.” This is how sound beats are characterized. It is important to remember that, unlike standing waves, phase coincidences of peaks do not occur constantly, but at certain time intervals. To the ear, this pattern of beats is distinguished quite clearly, and is heard as a periodic increase and decrease in volume, respectively. The mechanism by which this effect occurs is extremely simple: when the peaks coincide, the volume increases, and when the valleys coincide, the volume decreases.
Standing waves arise in the case of superposition of two waves of the same amplitude, phase and frequency, when when such waves “meet” one moves in the forward direction and the other in the opposite direction. In the area of space (where the standing wave was formed), a picture of the superposition of two frequency amplitudes appears, with alternating maxima (the so-called antinodes) and minima (the so-called nodes). When this phenomenon occurs, the frequency, phase and attenuation coefficient of the wave at the place of reflection are extremely important. Unlike traveling waves, there is no energy transfer in a standing wave due to the fact that the forward and backward waves that form this wave transfer energy in equal quantities in both the forward and opposite directions. To clearly understand the occurrence of a standing wave, let’s imagine an example from home acoustics. Let's say we have floor-standing speakers in some limited space (room). Having them play something with a lot of bass, let's try to change the location of the listener in the room. Thus, a listener who finds himself in the zone of minimum (subtraction) of a standing wave will feel the effect that there is very little bass, and if the listener finds himself in a zone of maximum (addition) frequencies, then the opposite effect of a significant increase in the bass region is obtained. In this case, the effect is observed in all octaves of the base frequency. For example, if the base frequency is 440 Hz, then the phenomenon of “addition” or “subtraction” will also be observed at frequencies of 880 Hz, 1760 Hz, 3520 Hz, etc.
Resonance phenomenon
Most solids have a natural resonance frequency. It is quite easy to understand this effect using the example of an ordinary pipe, open at only one end. Let's imagine a situation where a speaker is connected to the other end of the pipe, which can play one constant frequency, which can also be changed later. So, the pipe has its own resonance frequency, in simple terms - this is the frequency at which the pipe “resonates” or makes its own sound. If the frequency of the speaker (as a result of adjustment) coincides with the resonance frequency of the pipe, then the effect of increasing the volume several times will occur. This happens because the loudspeaker excites vibrations of the air column in the pipe with a significant amplitude until the same “resonant frequency” is found and the addition effect occurs. The resulting phenomenon can be described as follows: the pipe in this example “helps” the speaker by resonating at a specific frequency, their efforts add up and “result” in an audible loud effect. This phenomenon can easily be seen in the example of musical instruments, since the design of most instruments contains elements called resonators. 
It is not difficult to guess what serves the purpose of enhancing a certain frequency or musical tone. For example: a guitar body with a resonator in the form of a hole mating with the volume; The design of the flute tube (and all pipes in general); The cylindrical shape of the drum body, which itself is a resonator of a certain frequency.
Frequency spectrum of sound and frequency response
Since in practice there are practically no waves of the same frequency, it becomes necessary to decompose the entire sound spectrum of the audible range into overtones or harmonics. For these purposes, there are graphs that display the dependence of the relative energy of sound vibrations on frequency. This graph is called a sound frequency spectrum graph. Frequency spectrum of sound There are two types: discrete and continuous. A discrete spectrum plot displays individual frequencies separated by blank spaces. The continuous spectrum contains all sound frequencies at once. 
In the case of music or acoustics, the usual graph is most often used Amplitude-Frequency Characteristics(abbreviated as "AFC"). This graph shows the dependence of the amplitude of sound vibrations on frequency throughout the entire frequency spectrum (20 Hz - 20 kHz). Looking at such a graph, it is easy to understand, for example, the strengths or weaknesses of a particular speaker or acoustic system as a whole, the strongest areas of energy output, frequency dips and rises, attenuation, and also to trace the steepness of the decline.
Propagation of sound waves, phase and antiphase
The process of propagation of sound waves occurs in all directions from the source. The simplest example to understand this phenomenon is a pebble thrown into water. 
From the place where the stone fell, waves begin to spread across the surface of the water in all directions. However, let’s imagine a situation using a speaker in a certain volume, say a closed box, which is connected to an amplifier and plays some kind of musical signal. It is easy to notice (especially if you apply a powerful low-frequency signal, for example a bass drum) that the speaker makes a rapid movement “forward”, and then the same rapid movement “backward”. What remains to be understood is that when the speaker moves forward, it emits a sound wave that we hear afterwards. But what happens when the speaker moves backward? And paradoxically, the same thing happens, the speaker makes the same sound, only in our example it propagates entirely within the volume of the box, without going beyond its limits (the box is closed). In general, in the above example one can observe quite a lot of interesting physical phenomena, the most significant of which is the concept of phase.
The sound wave that the speaker, being in the volume, emits in the direction of the listener is “in phase”. The reverse wave, which goes into the volume of the box, will be correspondingly antiphase. All that remains is to understand what these concepts mean? Signal phase– this is the sound pressure level at the current moment in time at some point in space. The easiest way to understand phase is through the example of reproducing musical material with a conventional floor-standing stereo pair of home speaker systems. Let's imagine that two such floor-standing speakers are installed in a certain room and play. In this case, both acoustic systems reproduce a synchronous signal of variable sound pressure, and the sound pressure of one speaker is added to the sound pressure of the other speaker. A similar effect occurs due to the synchronicity of signal reproduction from the left and right speakers, respectively, in other words, the peaks and troughs of the waves emitted by the left and right speakers coincide.
Now let’s imagine that the sound pressures still change in the same way (have not undergone changes), but only now they are opposite to each other. This can happen if you connect one speaker system out of two in reverse polarity ("+" cable from the amplifier to the "-" terminal of the speaker system, and "-" cable from the amplifier to the "+" terminal of the speaker system). In this case, the opposite signal will cause a pressure difference, which can be represented in numbers as follows: the left speaker will create a pressure of “1 Pa”, and the right speaker will create a pressure of “minus 1 Pa”. As a result, the total sound volume at the listener's location will be zero. This phenomenon is called antiphase. If we look at the example in more detail for understanding, it turns out that two speakers playing “in phase” create identical areas of air compaction and rarefaction, thereby actually helping each other. In the case of an idealized antiphase, the area of compressed air space created by one speaker will be accompanied by an area of rarefied air space created by the second speaker. This looks approximately like the phenomenon of mutual synchronous cancellation of waves. True, in practice the volume does not drop to zero, and we will hear a highly distorted and weakened sound.
The most accessible way to describe this phenomenon is as follows: two signals with the same oscillations (frequency), but shifted in time. In view of this, it is more convenient to imagine these displacement phenomena using the example of an ordinary round clock. Let's imagine that there are several identical round clocks hanging on the wall. When the second hands of this watch run synchronously, on one watch 30 seconds and on the other 30, then this is an example of a signal that is in phase. If the second hands move with a shift, but the speed is still the same, for example, on one watch it is 30 seconds, and on another it is 24 seconds, then this is a classic example of a phase shift. In the same way, phase is measured in degrees, within a virtual circle. In this case, when the signals are shifted relative to each other by 180 degrees (half a period), classical antiphase is obtained. Often in practice, minor phase shifts occur, which can also be determined in degrees and successfully eliminated.
Waves are plane and spherical. A plane wave front propagates in only one direction and is rarely encountered in practice. A spherical wavefront is a simple type of wave that originates from a single point and travels in all directions. Sound waves have the property diffraction, i.e. ability to go around obstacles and objects. The degree of bending depends on the ratio of the sound wavelength to the size of the obstacle or hole. Diffraction also occurs when there is some obstacle in the path of sound. In this case, two scenarios are possible: 1) If the size of the obstacle is much larger than the wavelength, then the sound is reflected or absorbed (depending on the degree of absorption of the material, the thickness of the obstacle, etc.), and an “acoustic shadow” zone is formed behind the obstacle. . 2) If the size of the obstacle is comparable to the wavelength or even less than it, then the sound diffracts to some extent in all directions. If a sound wave, while moving in one medium, hits the interface with another medium (for example, an air medium with a solid medium), then three scenarios can occur: 1) the wave will be reflected from the interface 2) the wave can pass into another medium without changing direction 3) a wave can pass into another medium with a change in direction at the boundary, this is called “wave refraction”.
The ratio of the excess pressure of a sound wave to the oscillatory volumetric velocity is called wave resistance. In simple words, wave impedance of the medium can be called the ability to absorb sound waves or “resist” them. The reflection and transmission coefficients directly depend on the ratio of the wave impedances of the two media. Wave resistance in a gaseous medium is much lower than in water or solids. Therefore, if a sound wave in air strikes a solid object or the surface of deep water, the sound is either reflected from the surface or absorbed to a large extent. This depends on the thickness of the surface (water or solid) on which the desired sound wave falls. When the thickness of a solid or liquid medium is low, sound waves almost completely “pass”, and vice versa, when the thickness of the medium is large, the waves are more often reflected. In the case of reflection of sound waves, this process occurs according to a well-known physical law: “The angle of incidence is equal to the angle of reflection.” In this case, when a wave from a medium with a lower density hits the boundary with a medium of higher density, the phenomenon occurs refraction. It consists in the bending (refraction) of a sound wave after “meeting” an obstacle, and is necessarily accompanied by a change in speed. Refraction also depends on the temperature of the medium in which reflection occurs.
In the process of propagation of sound waves in space, their intensity inevitably decreases; we can say that the waves attenuate and the sound weakens. In practice, encountering a similar effect is quite simple: for example, if two people stand in a field at some close distance (a meter or closer) and start saying something to each other. If you subsequently increase the distance between people (if they begin to move away from each other), the same level of conversational volume will become less and less audible. This example clearly demonstrates the phenomenon of a decrease in the intensity of sound waves. Why is this happening? The reason for this is various processes of heat exchange, molecular interaction and internal friction of sound waves. Most often in practice, sound energy is converted into thermal energy. Such processes inevitably arise in any of the 3 sound propagation media and can be characterized as absorption of sound waves.
The intensity and degree of absorption of sound waves depends on many factors, such as pressure and temperature of the medium. Absorption also depends on the specific sound frequency. When a sound wave propagates through liquids or gases, a friction effect occurs between different particles, which is called viscosity. As a result of this friction at the molecular level, the process of converting a wave from sound to heat occurs. In other words, the higher the thermal conductivity of the medium, the lower the degree of wave absorption. Sound absorption in gaseous media also depends on pressure (atmospheric pressure changes with increasing altitude relative to sea level). As for the dependence of the degree of absorption on the frequency of sound, taking into account the above-mentioned dependences of viscosity and thermal conductivity, the higher the frequency of sound, the higher the absorption of sound. For example, at normal temperature and pressure in air, the absorption of a wave with a frequency of 5000 Hz is 3 dB/km, and the absorption of a wave with a frequency of 50,000 Hz will be 300 dB/m.
In solid media, all the above dependencies (thermal conductivity and viscosity) are preserved, but several more conditions are added to this. They are associated with the molecular structure of solid materials, which can be different, with its own inhomogeneities. Depending on this internal solid molecular structure, the absorption of sound waves in this case can be different, and depends on the type of specific material. When sound passes through a solid body, the wave undergoes a number of transformations and distortions, which most often leads to the dispersion and absorption of sound energy. At the molecular level, a dislocation effect can occur when a sound wave causes a displacement of atomic planes, which then return to their original position. Or, the movement of dislocations leads to a collision with dislocations perpendicular to them or defects in the crystal structure, which causes their inhibition and, as a consequence, some absorption of the sound wave. However, the sound wave can also resonate with these defects, which will lead to distortion of the original wave. The energy of the sound wave at the moment of interaction with the elements of the molecular structure of the material is dissipated as a result of internal friction processes.
In this article I will try to analyze the features of human auditory perception and some of the subtleties and features of sound propagation.
Thunderclaps, music, the sound of the surf, human speech and everything else that we hear is sound. What is "sound"?
Image source: pixabay.com
In fact, everything that we are accustomed to consider as sound is just one of the types of vibrations (air) that our brain and organs can perceive.
What is the nature of sound
All sounds propagated in the air are vibrations of a sound wave. It arises through the vibration of an object and diverges from its source in all directions. The vibrating object compresses the molecules in the environment and then creates a rarefied atmosphere, causing the molecules to repel each other further and further. Thus, changes in air pressure propagate away from the object, the molecules themselves remain in an unchanged position for themselves.
The effect of sound waves on the eardrum. Image source: prd.go.th
As a sound wave travels through space, it reflects off objects in its path, creating changes in the surrounding air. When these changes reach your ear and affect the eardrum, the nerve endings send a signal to the brain, and you perceive these vibrations as sound.
Basic characteristics of a sound wave
The simplest sound wave shape is a sine wave. Sine waves in their pure form are rarely found in nature, but it is with them that one should begin to study the physics of sound, since any sounds can be decomposed into a combination of sine waves.
A sine wave clearly demonstrates the three main physical criteria of sound - frequency, amplitude and phase.
Frequency
The lower the vibration frequency, the lower the sound, Image source: ReasonGuide.Ru
Frequency is a quantity that characterizes the number of vibrations per second. It is measured in the number of oscillation periods or in hertz (Hz). The human ear can perceive sound in the range from 20 Hz (low frequencies) to 20 KHz (high frequencies). Sounds above this range are called ultrasound, and below - infrasound, and are not perceived by human hearing.
Amplitude
The greater the amplitude of the sound wave, the louder the sound.
The concept of amplitude (or intensity) of a sound wave refers to the strength of the sound, which the human hearing senses as the volume or loudness of the sound. People can perceive a fairly wide range of sound volumes: from a dripping faucet in a quiet apartment to music playing at a concert. To measure loudness, phonometers (measured in decibels) are used, which use a logarithmic scale to make measurements more convenient.
Sound wave phase
Phases of a sound wave. Image source: Muz-Flame.ru
Used to describe the properties of two sound waves. If two waves have the same amplitude and frequency, then the two sound waves are said to be in phase. Phase is measured from 0 to 360, where 0 is a value indicating that the two sound waves are synchronous (in phase) and 180 is a value indicating that the waves are opposite to each other (out of phase). When two sound waves are in phase, the two sounds overlap and the signals reinforce each other. When two signals that do not match in amplitude are combined, the signals are suppressed due to the difference in pressure, which leads to a zero result, that is, the sound disappears. This phenomenon is known as “phase suppression.”
When combining two identical audio signals, phase cancellation can become a serious problem, and combining the original sound wave with the wave reflected from surfaces in the acoustic room is also a huge nuisance. For example, when the left and right channels of a stereo mixer are combined to produce a harmonious recording, the signal may suffer from phase cancellation.
What is a decibel?
Decibels measure the level of sound pressure or electrical voltage. This is a unit that shows the ratio of two different quantities to each other. Bel (named after the American scientist Alexander Bell) is a decimal logarithm that reflects the ratio of two different signals to each other. This means that for each subsequent bel in the scale, the received signal is ten times stronger. For example, the sound pressure of a loud sound is billions of times higher than that of a quiet sound. In order to display such large values, they began to use the relative value of decibels (dB) - with 1,000,000,000 being 109, or simply 9. The adoption of this value by physicists and acousticians made it possible to make working with huge numbers more convenient.
Volume scale for different sounds. Image source: Nauet.ru
In practice, the bel is too large a unit for measuring sound level, so the decibel, which is one tenth of a bel, was used instead. It cannot be said that using decibels instead of bels is like using, say, centimeters instead of meters to indicate shoe size; bels and decibels are relative values.
From the above it is clear that sound level is usually measured in decibels. Some sound level standards have been used in acoustics for many years, from the invention of the telephone to the present day. Most of these standards are difficult to apply with respect to modern equipment; they are used only for outdated pieces of equipment. Today, equipment in recording and broadcast studios uses a unit such as dBu (decibel relative to the level of 0.775 V), and in household equipment - dBV (decibel measured relative to the level of 1 V). Digital audio equipment uses dBFS (decibel full scale) to measure sound power.
dBm– “m” stands for milliwatts (mW), a unit of measurement used to denote electrical power. It is necessary to distinguish power from electrical voltage, although these two concepts are closely related to each other. The dBm unit of measurement began to be used at the dawn of the introduction of telephone communications, and today it is also used in professional equipment.
dBu- in this case, voltage is measured (instead of power) relative to the reference zero level; 0.75 volts is considered to be the reference level. When working with modern professional audio equipment, dBu is replaced by dBm. It was more convenient to use dBu as a unit of measurement in the field of audio engineering in the past, when it was more important to count electrical power rather than voltage to evaluate signal strength.
dBV– this unit of measurement is also based on the reference zero level (as in the case of dBu), however, 1 V is taken as the reference level, which is more convenient than the figure of 0.775 V. This unit of sound measurement is often used for household and semi-professional audio equipment.
dBFS– this signal level rating is widely used in digital audio engineering and is very different from the above units of measurement. FS (full scale) is a full scale that is used because, unlike an analog audio signal, which has an optimal voltage, the entire range of digital values is equally acceptable when working with a digital signal. 0 dBFS is the highest possible digital audio signal level that can be recorded without distortion. Analogue measurement standards such as dBu and dBV have no dynamic range headroom beyond 0 dBFS.
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Sound is mechanical vibrations that propagate in an elastic material medium primarily in the form of longitudinal waves.
In a vacuum, sound does not propagate, since sound transmission requires a material medium and mechanical contact between particles of the material medium.
In a medium, sound travels in the form of sound waves. Sound waves are mechanical vibrations that are transmitted in a medium using its conditional particles. Conventional particles of a medium mean its microvolumes.
Basic physical characteristics of an acoustic wave:
1. Frequency.
Frequency sound wave is the magnitude equal to the number of complete oscillations per unit time. Indicated by the symbol v (nude) and measured in hertz. 1 Hz = 1 count/sec = [ s -1 ].
The sound vibration scale is divided into the following frequency intervals:
· infrasound (from 0 to 16 Hz);
· audible sound (from 16 to 16,000 Hz);
· ultrasound (over 16,000 Hz).
The frequency of a sound wave is closely related to its inverse quantity – the period of the sound wave. Period A sound wave is the time of one complete oscillation of the particles of the medium. Designated T and is measured in seconds [s].
According to the direction of vibration of the particles of the medium carrying the sound wave, sound waves are divided into:
· longitudinal;
· transverse.
For longitudinal waves, the direction of vibration of the particles of the medium coincides with the direction of propagation of the sound wave in the medium (Fig. 1).
For transverse waves, the directions of vibration of the particles of the medium are perpendicular to the direction of propagation of the sound wave (Fig. 2).
Rice. 1 Fig. 2
Longitudinal waves propagate in gases, liquids and solids. Transverse - only in solids.
3. Shape of vibrations.
According to the form of vibrations, sound waves are divided into:
· simple waves;
complex waves.
The graph of a simple wave is a sine wave.
The graph of a complex wave is any periodic non-sinusoidal curve .
4. Wavelength.
Wavelength is the quantity equal to the distance over which a sound wave travels in a time equal to one period. It is designated λ (lambda) and is measured in meters (m), centimeters (cm), millimeters (mm), micrometers (µm).
The wavelength depends on the medium in which the sound travels.
5. Sound wave speed.
Sound wave speed is the speed of sound propagation in a medium with a stationary sound source. Denoted by the symbol v, calculated by the formula:
The speed of the sound wave depends on the type of medium and temperature. The speed of sound is highest in solid elastic bodies, less in liquids, and lowest in gases.
air, normal atmospheric pressure, temperature - 20 degrees, v = 342 m/s;
water, temperature 15-20 degrees, v = 1500 m/s;
metals, v = 5000-10000 m/s.
The speed of sound in air increases by about 0.6 m/s with an increase in temperature of 10 degrees.
