This article discusses such a phenomenon of physics as interference: what it is, when it occurs and how it is applied. It also describes in detail the related concept of wave physics - diffraction.

Wave types

When the word “wave” appears in a book or in a conversation, then, as a rule, the sea immediately appears: a blue expanse, an immense distance, one after another, salty shafts run onto the shore. An inhabitant of the steppes will imagine a different view: a boundless expanse of grass, it sways under a gentle breeze. Someone else will remember the waves, looking at the folds of a heavy curtain or the fluttering of a flag on a sunny day. A mathematician will think of a sinusoid, a radio lover will think of electromagnetic oscillations. All of them have a different nature and belong to different species. But one thing is undeniable: a wave is a state of deviation from equilibrium, the transformation of some kind of “smooth” law into an oscillatory one. It is for them that such a phenomenon as interference is applicable. What is it and how it arises, we will consider a little later. First, let's look at what waves are. We list the following types:

• mechanical;
• chemical;
• electromagnetic;
• gravity;
• spin;
• probabilistic.

From a physics point of view, waves carry energy. But it happens that the mass also moves. Answering the question of what interference is in physics, it should be noted that it is characteristic of waves of absolutely any nature.

Wave Difference Signs

Oddly enough, but there is no single definition of a wave. Their species are so diverse that there are more than a dozen types of classification alone. How are waves distinguished?

1. According to the method of distribution in the environment (running or standing).
2. By the nature of the wave itself (oscillatory and solitons are different precisely on this basis).
3. According to the type of distribution in the medium (longitudinal, transverse).
4. By degree of linearity (linear or non-linear).
5. According to the properties of the medium in which they propagate (discrete, continuous).
6. In shape (flat, spherical, spiral).
7. According to the features of the physical propagation medium (mechanical, electromagnetic, gravitational).
8. In the direction of oscillation of the particles of the medium (compression or shear waves).
9. By the time it takes to excite the medium (single, monochromatic, wave packet).

And interference is applicable to any type of these perturbations of the medium. What is so special about this concept and why exactly this phenomenon makes our world the way it is, we will tell after giving the characteristics of the wave.

Wave characteristics

Regardless of the type and type of waves, they all have common characteristics. Here is the list:

1. The comb is a kind of maximum. For compression waves, this is the place of the highest density of the medium. Represents the largest positive deviation of the oscillation from the equilibrium state.
2. A hollow (in some cases a valley) is the opposite of a ridge. The minimum, the largest negative deviation from the equilibrium state.
3. Temporal periodicity, or frequency, is the time it takes for a wave to travel from one high to the next.
4. Spatial periodicity, or wavelength, is the distance between adjacent peaks.
5. Amplitude is the height of the peaks. It is this definition that will be needed to understand what wave interference is.

We examined the wave in great detail, its characteristics and various classifications, because the concept of "interference" cannot be explained without a clear understanding of such a phenomenon as a disturbance of the medium. We remind you that interference only makes sense for waves.

Wave interaction

Now we have come close to the concept of "interference": what is it, when does it occur and how to define it. All the types, types and characteristics of waves listed above referred to the ideal case. These were descriptions of a "spherical horse in a vacuum", that is, some theoretical constructions that are impossible in the real world. But in practice, the entire space around is permeated with various waves. Light, sound, heat, radio, chemical processes are media. And all these waves interact. One feature should be noted: in order for them to influence each other, they must have similar characteristics.

Sound waves can't interfere with light in any way, and radio waves can't interact with wind in any way. Of course, the influence is still there, but it is so small that its effect is simply not taken into account. In other words, when explaining what light interference is, it is assumed that one photon affects another when it meets. So, in more detail.

Interference

For many types of waves, the principle of superposition operates: when they meet at one point in space, they interact. The exchange of energy is displayed on the change in amplitude. The law of interaction is as follows: if two maxima meet at one point, then in the final wave the intensity of the maximum doubles; if a maximum and a minimum meet, then the resulting amplitude vanishes. This is a clear answer to the question of what is the interference of light and sound. In essence, this is a superimposition phenomenon.

Interference of waves with different characteristics

The event described above represents the meeting of two identical waves in linear space. However, two counterpropagating waves can have different frequencies, amplitudes, and lengths. How to present the final picture in this case? The answer lies in the fact that the result will not be exactly like a wave. That is, the strict order of alternation of maxima and minima will be violated: at some point the amplitude will be maximum, at the next it will be less, then the maximum and minimum will meet and the result will turn to zero. However, no matter how strong the differences between the two waves, the amplitude will still repeat itself sooner or later. In mathematics, it is customary to speak of infinity, but in reality, frictional forces and inertia can stop the very existence of the resulting wave before the pattern of peaks, valleys and plains is repeated.

Interference of waves meeting at an angle

But, in addition to their own characteristics, real waves can have different positions in space. For example, when considering what sound interference is, this must be taken into account. Imagine: a boy is walking and blowing a whistle. It sends a sound wave ahead of itself. And another boy on a bicycle passes by him and rings a bell so that the pedestrian moves aside. At the meeting point of these two sound waves, they intersect at some angle. How to calculate the amplitude and shape of the final fluctuation of the air, which will reach, for example, the nearest seller of seeds of grandmother Masha? This is where the vector component of the sound wave comes into play. And in this case, it is necessary to add or subtract not only the magnitude of the amplitude, but also the propagation vectors of these oscillations. We hope that Grandma Masha will not scream too much at the noisy guys.

Interference of light with different polarization

It also happens that photons of different polarizations meet at one point. In this case, the vector component of electromagnetic oscillations should also be taken into account. If they are not mutually perpendicular or one of the beams of light has a circular or elliptical polarization, then the interaction is quite possible. Several methods for determining the optical purity of crystals are based on this principle: there should be no interaction in perpendicularly polarized beams. If the picture is distorted, then the crystal is not ideal, it changes the polarization of the beams, which means that it was not grown correctly.

Interference and diffraction

The interaction of two beams of light leads to their interference, as a result, the observer sees a number of light (maxima) and dark (minimum) bands or rings. But the interaction of light and matter is accompanied by another phenomenon - diffraction. It is based on the fact that light of different wavelengths is refracted differently by the medium. For example, if the wavelength is 300 nanometers, then the deflection angle is 10 degrees, and if 500 nanometers, it is already 12. Thus, when light from a sunbeam falls on a quartz prism, red is refracted differently than violet (their wavelengths differ) , and the observer sees a rainbow. This is the answer to the question of what is interference and diffraction of light and how they differ. If monochromatic radiation from a laser is directed to the same prism, there will be no rainbow, since there are no photons of different wavelengths. It's just that the beam will deviate from the original direction of propagation by a certain angle, and that's it.

Application of the phenomenon of interference in practice

There are a lot of opportunities to get practical benefit from this purely theoretical phenomenon. Only the main ones will be listed here:

1. Study of the quality of crystals. We talked about this a little higher.
2. Identification of lens errors. Often they must be ground into a perfect spherical shape. The presence of any defects is detected precisely with the help of the phenomenon of interference.
3. Determination of film thickness. In some types of production, a constant film thickness, such as plastic, is very important. It is precisely the phenomenon of interference together with diffraction that makes it possible to determine its quality.
4. Illumination of optics. Glasses, lenses of cameras and microscopes are covered with a thin film. Thus, electromagnetic waves of a certain length are simply reflected and superimposed on themselves, reducing interference. Most often, enlightenment is done in the green part of the optical spectrum, since it is this area that the human eye perceives best.
5. Space exploration. Knowing the laws of interference, astronomers are able to separate the spectra of two closely spaced stars and determine their compositions and distance from the Earth.
6. Theoretical research. Once it was with the help of the phenomenon of interference that it was possible to prove the wave nature of elementary particles, such as electrons and protons. This confirmed the hypothesis of corpuscular-wave dualism of the microworld and laid the foundation for the quantum era.

We hope that with this article, your knowledge of the superposition of coherent (emitted by sources that have a constant phase difference and the same frequency) waves has expanded significantly. This phenomenon is called interference.

Wave nature of light. In the 17th century, the Dutch scientist Christian Huygens suggested that light has a wave nature. If the size of the object is commensurate with the wavelength, then the light, as it were, runs into the shadow area and the shadow boundary is blurred. These phenomena cannot be explained by the rectilinear propagation of light. The idea contradicted the statements of I. Newton that light is a stream of particles, but the wave nature of light was experimentally confirmed in such phenomena as interference and diffraction.

These wave phenomena can be explained using two concepts: the Huygens principle and the coherence of light.

Huygens principle.Huygens principle is as follows: any point of the wave front can be considered as a secondary source of elementary waves propagating in the original direction at the speed of the primary wave. Thus, the primary wave can be considered as the sum of secondary elementary waves. According to the Huygens principle, the new position of the wave front of the primary wave coincides with the envelope curve from the elementary secondary waves (Fig. 11.20).

Rice. 11.20. Huygens principle.

Coherence. For the occurrence of diffraction and interference, the condition of constancy of the phase difference of light waves from different light sources must be observed:

Waves that maintain a constant phase difference are called coherent.

Wave phase is a function of distance and time:

The main condition for coherence is the constancy of the frequency of light. However, light is not strictly monochromatic in reality. Therefore, the frequency, and, consequently, the phase difference of light may not depend on one of the parameters (either on time or on distance). If the frequency does not depend on time, the coherence is called temporal, and when does not depend on the distance - spatial. In practice, it looks like that the interference or diffraction pattern on the screen either does not change in time (with temporal coherence), or it is preserved when the screen moves in space (with spatial coherence).

Light interference. In 1801, the English physicist, physician and astronomer T. Jung (1773 - 1829) received convincing confirmation of the wave nature of light and measured the wavelength of light. The scheme of Young's experience is shown in Fig. 11.21. Instead of the expected two lines if the light were particles, he saw a series of alternating bands. This could be explained by assuming that light is a wave.

Light interference called the phenomenon of wave superposition. Light interference is characterized by the formation of a stationary (constant in time) interference pattern - a regular alternation in space of areas of increased and reduced light intensity, resulting from the superposition of coherent light waves, i.e. waves of the same frequency, having a constant phase difference.

It is practically impossible to achieve a constant difference in the phases of waves from independent sources. Therefore, the following method is usually used to obtain coherent light waves. Light from one source is somehow divided into two or more beams and, having sent them along different paths, they are then brought together. The interference pattern observed on the screen depends on the difference between the paths of these waves.

Conditions for interference maxima and minima. The superposition of two waves with the same frequency and constant phase difference leads to the appearance on the screen, for example, when light hits two slits, an interference pattern - alternation of light and dark stripes on the screen. The reason for the appearance of light bands is the superposition of two waves in such a way that two maxima are added at a given point. When the maximum and minimum of the wave are superimposed at a given point, they compensate each other and a dark band appears. Figures 11.22a and 11.22b illustrate the conditions for the formation of minima and maxima of light intensity on the screen. To explain these facts on a quantitative level, we introduce the notation: Δ is the path difference, d is the distance between two slits, is the wavelength of light. In this case, the maximum condition, which is illustrated in Fig. 11.22b, represents the multiplicity of the path difference and the wavelength of light:

This will happen if the oscillations excited at point M by both waves occur in the same phase and the phase difference is:

where m=1, 2, 3, ….

The condition for the appearance of minima on the screen represents the multiplicity of light half-waves:

(11.4.5)

In this case, the oscillations of light waves excited by both coherent waves at point M in Fig. 11.22a will occur in antiphase with a phase difference:

(11.4.6)

Rice. 11.21. Conditions for the formation of minima and maxima of the interference pattern

An example of interference is interference in thin films. It is well known that if you drop gasoline or oil on water, colored stains will be noticeable. This is due to the fact that gasoline or oil forms a thin film on the water. Part of the light is reflected from the upper surface, and the other part from the lower surface - the interface between the two media. These waves are coherent. Rays reflected from the upper and lower surfaces of the film (Fig. 11.22) interfere, forming maxima and minima. Thus, an interference pattern appears on a thin film. A change in the thickness of the film of gasoline or oil on the surface of the water leads to a change in the path difference for waves of different lengths and, consequently, a change in the color of the stripes.

Rice. 11.22 Interference in thin films

One of the most important achievements in the use of interference is the creation of an ultra-precise instrument for measuring distances - Michelson interferometer(fig.11.24). Monochromatic light is incident on a semitransparent mirror located in the center of the pattern, which splits the beam. One beam of light is reflected from a fixed mirror, located at the top of Fig. 11.23, the second from a movable mirror, located on the right in Fig. 11.23. Both beams return to the observation point, interfering with each other on the light wave interference recorder. The displacement of the movable mirror by a quarter of a wave leads to the replacement of light bands by dark ones. The distance measurement accuracy achieved in this case is 10 -4 mm. This is one of the most accurate methods for measuring the size of microscopic quantities, which allows you to measure distances with an accuracy comparable to the wavelength of light.

Adjustment of modern high-tech installations, for example, elements of the Large Hadron Collider at CERN, takes place with an accuracy of up to wavelengths of light.

Rice. 11.23. Michelson interferometer

Diffraction. The experimental discovery of the phenomenon of diffraction was another confirmation of the validity of the wave theory of light.

In the Paris Academy of Sciences in 1819, A. Fresnel presented the wave theory of light, which explained the phenomenon of diffraction and interference. According to the wave theory, the diffraction of light on an opaque disk should lead to the appearance of a bright spot in the center of the disk, since the difference in the path of the rays in the center of the disk is zero. The experiment confirmed this assumption (Fig. 11.24). According to Huygens' theory, points on the disk rim are sources of secondary light waves, and they are coherent with each other. Therefore, light enters the region behind the disk.

Diffraction called the phenomenon of wave bending around obstacles. If the wavelength is large, then the wave does not seem to notice the obstacles. If the wavelength is comparable to the size of the obstacle, then on the screen the border of the shadow from the obstacle will be blurred.

Rice. 11.24. Diffraction on an opaque disk

The diffraction of light by a single slit results in the appearance of alternating light and dark bands. Moreover, the condition of the first minimum has the form (Fig. 11.25):

where is the wavelength, d is the size of the slot.

The same figure shows the dependence of the light intensity on the deviation angle θ from the rectilinear direction.

Rice. 11.25. The condition for the formation of the 1st maximum.

A simple example of diffraction can be observed by yourself, if you look at a room bulb through a small slit in the palm of your hand or through the eye of a needle, then we will notice concentric multi-colored circles around the light source.

Based on the use of the phenomenon of diffraction works spectroscope- a device for very accurate measurement of wavelengths using a diffraction grating (Fig. 11.26).

Rice. 11.26. Spectroscope.

The spectroscope was invented by Josef Fraunhofer in the early 19th century. In it, the light that passed through the slits and collimating lenses turned into a thin beam of parallel rays. The light from the source enters the collimator through a narrow slit. The slit is in the focal plane. The telescope examines the diffraction grating. If the angle of the pipe coincides with the angle directed to the maximum (usually the first one), then the observer will see a bright band. The angle θ of the location on the screen of the first maximum determines the wavelength. In essence, this device is based on the principle illustrated in Fig. 11.25.

To obtain the dependence of the light intensity on the wavelength (this dependence is called the spectrum), the light was passed through a prism. At the exit from it, as a result of dispersion, the light was split into components. With the help of a telescope it is possible to measure the emission spectra. After the invention of photographic film, a more precise instrument was created: the spectrograph. Working on the same principle as the spectroscope, he had a camera instead of an observation tube. In the mid-twentieth century, the camera was replaced by an electron photomultiplier tube, which made it possible to significantly increase accuracy and conduct real-time analysis.

The phenomena of interference and diffraction of light serve as proof of its wave nature.

interference waves is called the phenomenon of superposition of waves, in which their mutual amplification occurs at some points in space and weakening at others. A time-constant (stationary) interference pattern arises only when waves of equal frequency with a constant phase difference are added. Such waves and the sources that excite them are called coherent.

Light interference - one of the manifestations of its wave nature, occurs, for example, when light is reflected in a thin air gap between a flat glass plate and a plano-convex lens. In this case, interference occurs when the coherent waves are added 1 and 2 reflected from both sides of the air layer. This interference pattern, which has the form of concentric rings, is called Newton's rings in honor of I. Newton, who first described it and found that the radii of these rings for red light are greater than for blue.

Considering that light is waves, the English physicist T. Jung explained the interference of light as follows. Ray incident on the lens 0 after reflection from its convex surface and refraction gives rise to two reflected rays ( 1 and 2 ). In this case, the light waves in the beam 2 lagging behind the beam 1 on Dj, and the phase difference Dj depends on the "extra" path that the beam has traveled 2 , compared to the beam 1 .

Obviously, if Dj = n l, where n is an integer, then the waves 1 and 2 , adding up, will reinforce each other and, looking at the lens at these angles, we will see a bright ring of light of a given wavelength. On the contrary, if

where n is an integer, then the waves 1 and 2 , adding up, will extinguish each other, and therefore, looking at the lens from above at such an angle, we will see a dark ring. Thus, wave interference leads to a redistribution of the oscillation energy between various closely spaced particles of the medium.

The interference depends on the wavelength, and therefore, by measuring the angular distances between adjacent minima and maxima of the interference pattern, one can determine the wavelength of light. If the interference occurs in thin films of gasoline on the surface of water or in films of soap bubbles, then this leads to the coloring of these films in all colors of the rainbow. Interference is used to reduce the reflection of light from optical glasses and lenses, which is called enlightenment of optics. To do this, a film of a transparent substance is applied to the glass surface of such a thickness that the phase difference of the light waves reflected from the glass and the film is .

Diffraction of light– the bending of light waves around the edges of obstacles, which is another proof of the wave nature of light, was first demonstrated by T. Jung in an experiment when a plane light wave fell on a screen with two closely spaced slits. According to the Huygens principle, slots can be considered as sources of secondary coherent waves. Therefore, passing through each of the slits, the light beam broadened, and an interference pattern in the form of alternating light and dark stripes was observed on the screen in the region of overlapping light beams from the slits. The appearance of the interference pattern is explained by the fact that the waves from the slots to each point P different distances r 1 and r 2 pass on the screen, and the corresponding phase difference between them determines the brightness of the point R.

Light polarization

The polarization of light waves, which is a consequence of their transverseness, changes upon reflection, refraction, and scattering of light in transparent media.

The transverseness of light waves is one of the consequences of the electromagnetic theory of J.K. Maxwell and is expressed in the fact that the vectors of the electric field strength oscillating in the waves E and magnetic field induction AT perpendicular to each other and to the direction of propagation of these waves. To describe an electromagnetic wave, it is enough to know how one of these two vectors changes, for example, E, which is called light vector. Light polarization name the orientation and nature of changes in the light vector in a plane perpendicular to the light beam. Light in which the directions of oscillation of the light vector are somehow ordered is called polarized.

If, during the propagation of an electromagnetic wave, the light vector retains its orientation, then such a wave is called linearly polarized or plane polarized, and the plane in which the light vector oscillates - vibration plane. An electromagnetic wave emitted by any atom (or molecule) in a single act of radiation is always linearly polarized. The source of linearly polarized light is also lasers.

If the plane of oscillation of an electromagnetic wave is constantly and randomly changing, then light is called unpolarized. Natural light (suns, lamps, candles, etc.) is the sum of the radiations of a huge number of individual atoms, each of which at a certain moment emits linearly polarized light waves. However, since the planes of oscillations of these light waves change randomly and are not coordinated with each other, the total light turns out to be unpolarized. Therefore, unpolarized light is often called natural.

If the amplitude of the light vector in one direction is greater than in the others, then such light is called partially polarized. Natural light, when reflected from non-metallic surfaces (water, glass, etc.), becomes partially polarized so that the amplitude of the light vector in a direction parallel to the reflecting plane becomes larger. The refraction of natural light at the boundary of two media also turns it into partially polarized, but in these cases, as a rule, the amplitude of the light vector in the direction parallel to the reflecting plane becomes smaller.

Natural light can be converted to linearly polarized using polarizers- devices that transmit waves with a light vector of only a certain direction. Tourmaline crystals are often used as polarizers, which strongly absorb rays with a light vector perpendicular to the optical axis of the crystal. Therefore, natural light passing through a tourmaline plate becomes linearly polarized with an electric vector oriented parallel to the tourmaline optical axis.

DEFINITION

interference called the change in the average energy flux density, which is caused by the superposition of waves.

Or a little differently: Interference is the addition of waves in space, and in this case, an amplitude distribution of total oscillations that is unchanged in time arises.

The interference of light waves is called the addition of waves, in which one can observe a time-stable pattern of amplification or weakening of the total vibrations of light at different spatial points. The term interference was introduced into science by T. Jung.

Interference Conditions

In order for a stable interference pattern to form when waves are superimposed, it is necessary that the wave sources have the same frequency and a constant phase difference. Such sources are called coherent (consistent). Coherent waves are called waves that are created by coherent sources.

Thus, only when coherent waves are superimposed, a stable interference pattern arises.

In optics, to create an interference pattern, coherent waves receive:

1. dividing the wave amplitude;
2. division of the wave front.

Interference minima condition

The amplitude of oscillations of interfering waves at the point under consideration will be minimal if the path difference () of the waves at this point contains an odd number of half-wave lengths ():

Let's assume that it fits on the segment, then it turns out that one wave lags behind the other by half a period. The phase difference of these waves turns out to be equal, which means that the oscillations occur in antiphase. When adding such oscillations, the amplitude of the total wave will be equal to zero.

Interference maxima condition

The amplitude of oscillations of interfering waves at the point under consideration will be maximum if the path difference () of the waves at this point contains an integer number of wavelengths ():

Definition of diffraction

DEFINITION

Deviation of waves from propagation in a straight line, rounding obstacles by a wave, is called diffraction.

The word diffraction from the Latin language means broken.

The phenomenon of diffraction is explained using the Huygens principle. Secondary waves, which are emitted by sections of the substance (medium), fall beyond the edges of the obstacle that is in the path of the wave. According to Fresnel's theory, the wave surface at any arbitrary moment of time is not only the envelope of secondary waves, but the result of their interference.

Conditions under which diffraction occurs

Diffraction is especially pronounced when the size of the obstacle is less than or comparable to the wavelength.

Waves of any nature can diffract, as well as interfere.

Intensity minima condition

When a light wave is diffracted by one slit at normal incidence of rays, the intensity minimum condition is written as:

where a is the slot width; - angle of diffraction; k - minimum number; - wavelength.

Intensity maxima condition

When a light wave is diffracted by one slit at normal incidence of rays, the intensity maximum condition is written as:

where is the approximate value of the diffraction angle.

The condition of the main intensity maxima during diffraction on a diffraction grating

The condition of the main intensity maxima of the diffraction of light on a diffraction grating at normal incidence of rays is written:

where d is the lattice period (constant); k is the number of the main maximum; is the angle between the normal to the grating plane and the direction of the diffracted waves.

Diffraction value

Diffraction does not make it possible to obtain clear images of small objects, since it is not always possible to assume that light propagates strictly in a straight line. As a result, images can be blurry, and magnification does not help to see the details of an object if its size is comparable to the wavelength of light. The phenomenon of diffraction imposes limits on the applicability of the laws of geometric optics and determines the limit of the resolution of optical instruments.

Examples of problem solving

EXAMPLE 1

Exercise

Why is it impossible to observe the phenomenon of interference with the help of two electric bulbs?

Decision

If you turn on one electric lamp, then add another one to it, then the illumination will increase, but there will be no alternations of dark and light stripes (minimums and maximums of illumination). This is because the light waves that are emitted by the lamps are not coherent (inconsistent). In order to obtain a time-stable interference pattern, light waves must have the same frequencies (wavelengths) and a phase difference that is constant in time. Atoms of light sources, such as lamps, emit waves independently of each other in separate trains. The trains of different sources are superimposed on each other. The oscillation amplitude at an arbitrary point in space changes chaotically in time, depending on the phase difference of wave trains. A stable distribution of highs and lows cannot be seen.

EXAMPLE 2

Exercise	A monochromatic beam of light with a wavelength m falls on a diffraction grating perpendicular to its surface. The number of lines per millimeter of the grating is 500. What is the highest order of the spectrum?
Decision	Let's make a drawing.

Interference is the sum of the vibrations. As a result of interference, at some points in space, the amplitude of oscillations increases, while at others, they decrease. An unchanged interference pattern is observed only when the difference between the summed oscillations is constant (they coherent ). Obviously, oscillations of the same frequency can be coherent. Therefore, interference is often studied monochromatic fluctuations.

Diffraction- call the phenomena associated with the property of waves to bend around obstacles, that is, to deviate from rectilinear propagation.

The figure on the right shows how sound waves change direction after passing through a hole in the wall. According to the Huygens principle, regions 1-5 become secondary sources of spherical sound waves. It can be seen that the secondary sources in regions 1 and 5 cause waves to go around obstacles.

Question 30.1

standing waves. Standing wave equation.

If several waves propagate in the medium, then the oscillations of the particles of the medium turn out to be the geometric sum of the oscillations that the particles would make during the propagation of each of the waves separately. The waves overlap Each other,without disturbing(without distorting each other). That's what it is principle of superposition of waves.

If two waves arriving at any point in space have a constant phase difference, such waves are called coherent. When coherent waves are added, interference phenomenon.

A very important case of interference is observed when two counterpropagating plane waves with the same amplitude are superimposed. The resulting oscillatory process is called standing wave . Practically standing waves arise when reflected from obstacles.

Let's write the equations of two plane waves propagating in opposite directions (initial phase):

The expression for the phase does not include the coordinate, so you can write:

The points of the medium located at the nodes do not oscillate.

The formation of standing waves is observed when the traveling and reflected waves interfere. At the boundary where the wave is reflected, an antinode is obtained if the medium from which the reflection occurs is less dense (Fig. 5.5, a), and the knot - if more dense (Fig. 5.5, b).

If we consider traveling wave , then in the direction of its propagation energy is transferred oscillatory movement. When same there is no standing wave of energy transfer , because incident and reflected waves of the same amplitude carry the same energy in opposite directions.

Question 32

Sound waves.

sound(or acoustic) waves are called elastic waves propagating in a medium with frequencies in the range of 16-20000 Hz. Waves of these frequencies, acting on the human hearing apparatus, cause the sensation of sound. Waves with n< 16 Гц (infrasonic) and n> 20 kHz ( ultrasonic) are not perceived by human hearing organs.

Sound waves in gases and liquids can only be longitudinal, since these media are elastic only with respect to compressive (tensile) deformations. In solids, sound waves can be both longitudinal and transverse, since solids are elastic with respect to compressive (tensile) and shear deformations.

sound intensity(or sound power) is the value determined by the time-averaged energy transferred by a sound wave per unit time through a unit area perpendicular to the direction of wave propagation:

Unit of sound intensity in SI - watt per square meter(W / m 2).

The sensitivity of the human ear is different for different frequencies. In order to cause a sound sensation, the wave must have a certain minimum intensity, but if this intensity exceeds a certain limit, then the sound is not heard and only causes pain. Thus, for each oscillation frequency, there is the smallest (threshold of hearing) and the greatest (pain threshold) the intensity of the sound that is capable of producing sound perception. On fig. 223 shows the dependence of the thresholds of hearing and pain on the frequency of the sound. The area between these two curves is hearing area.

If the intensity of sound is a quantity that objectively characterizes the wave process, then the subjective characteristic of sound associated with its intensity is sound volume, which depends on the frequency. According to the physiological law of Weber - Fechner, with increasing sound intensity, the volume increases according to the logarithmic law. On this basis, an objective assessment of the sound loudness is introduced according to the measured value of its intensity:

where I 0 - sound intensity at the threshold of hearing, taken for all sounds equal to 10 -12 W / m 2. Value L called sound intensity level and is expressed in bels (in honor of Bell's inventor of the telephone). Usually use units that are 10 times smaller, - decibels(dB).

The physiological characteristic of sound is volume level, which is expressed in backgrounds(background). The loudness for a sound at 1000 Hz (the frequency of a standard pure tone) is 1 phon if its intensity level is 1 dB. For example, noise in a subway car at high speed corresponds to »90 fon, and a whisper at a distance of 1 m - »20 fon.

Real sound is an overlay of harmonic oscillations with a large set of frequencies, i.e. sound has acoustic spectrum, which may be continuous(in a certain interval there are oscillations of all frequencies) and ruled(there are fluctuations of certain frequencies separated from each other).

The sound is characterized in addition to loudness by height and timbre. Pitch- sound quality, determined by a person subjectively by ear and depending on the frequency of the sound. As the frequency increases, the pitch of the sound increases, i.e., the sound becomes “higher”. The nature of the acoustic spectrum and the distribution of energy between certain frequencies determines the originality of the sound sensation, called timbre of sound. Thus, different singers who strike the same note have a different acoustic spectrum, that is, their voices have a different timbre.

Any body oscillating in an elastic medium with a sound frequency can be a sound source (for example, in stringed instruments, the sound source is a string connected to the body of the instrument).

Making oscillations, the body causes oscillations of the particles of the medium adjacent to it with the same frequency. The state of oscillatory motion is successively transferred to particles of the medium more and more distant from the body, i.e., a wave propagates in the medium with an oscillation frequency equal to the frequency of its source, and with a certain speed depending on the density and elastic properties of the medium. The speed of propagation of sound waves in gases is calculated by the formula

where R- molar gas constant, M - molar mass, g \u003d C p / C V - the ratio of the molar heat capacities of a gas at constant pressure and volume, T - thermodynamic temperature. From formula (158.1) it follows that the speed of sound in a gas does not depend on pressure R gas, but increases with temperature. The greater the molar mass of a gas, the lower the speed of sound in it. For example, when T\u003d 273 K the speed of sound in air ( M\u003d 29 × 10 -3 kg / mol) v=331 m/s, in hydrogen ( M\u003d 2 × 10 -3 kg / mol) v=1260 m/s. Expression (158.1) corresponds to experimental data.

When sound propagates in the atmosphere, it is necessary to take into account a number of factors: wind speed and direction, air humidity, the molecular structure of the gaseous medium, the phenomena of refraction and reflection of sound at the boundary of two media. In addition, any real medium has viscosity, so sound attenuation is observed, i.e., a decrease in its amplitude and, consequently, the intensity of a sound wave as it propagates. Sound attenuation is largely due to its absorption in the medium, associated with the irreversible transition of sound energy into other forms of energy (mainly heat).

For room acoustics, it is of great importance sound reverberation- the process of gradual attenuation of sound in enclosed spaces after turning off its source. If the rooms are empty, then the sound decays slowly and the room “booms” is created. If sounds fade quickly (when using sound-absorbing materials), then they are perceived as muffled. Reverb time- this is the time during which the intensity of the sound in the room is attenuated by a million times, and its level by 60 dB. The room has good acoustics if the reverberation time is 0.5-1.5 s.

Question 32.1

Pitch
In addition to loudness, sound is characterized by height. The pitch of a sound is determined by its frequency: the higher the frequency of vibrations in a sound wave, the higher the sound. Low frequency vibrations correspond to low sounds, high frequency vibrations correspond to high sounds.

So, for example, a bumblebee flaps its wings at a lower frequency than a mosquito: in a bumblebee it is 220 strokes per second, and in a mosquito - 500-600. Therefore, the flight of a bumblebee is accompanied by a low sound (buzz), and the flight of a mosquito is accompanied by a high sound (squeak).

A sound wave of a certain frequency is otherwise called a musical tone, so pitch is often referred to as pitch.

The main tone mixed with several vibrations of other frequencies forms a musical sound. For example, violin and piano sounds can include up to 15-20 different vibrations. Its timbre depends on the composition of each complex sound.

The frequency of free vibrations of a string depends on its size and tension. Therefore, by stretching the strings of the guitar with the help of pegs and pressing them to the neck of the guitar in different places, we change their natural frequency, and, consequently, the pitch of the sounds they make.

The nature of sound perception largely depends on the layout of the room in which speech or music is heard. This is explained by the fact that in closed rooms, the listener perceives, in addition to direct sound, also a continuous series of repetitions quickly following each other, caused by multiple reflections of sound from objects in the room, walls, ceiling and floor.

Question 32.2

sound power

sound power(relative) is an obsolete term describing a magnitude similar to, but not identical to, sound intensity. Approximately the same situation we observe for the intensity of light (unit - candela) - a quantity similar to the strength of radiation (unit - watt per steradian).

The sound intensity is measured on a relative scale from the threshold value, which corresponds to a sound intensity of 1 pW/m² with a sinusoidal signal frequency of 1 kHz and a sound pressure of 20 µPa. Compare this definition with the definition of the unit of luminous intensity: "a candela is equal to the intensity of light emitted in a given direction by a monochromatic source, at an emission frequency of 540 THz and an emission intensity in this direction of 1/683 W / sr."

Currently the term "power of sound" superseded by the term "audio volume level"