When a mechanical wave propagates, Mechanical waves: source, properties, formulas

Wave– the process of propagation of oscillations in an elastic medium.

mechanical wave– mechanical disturbances propagating in space and carrying energy.

Wave types:

longitudinal - particles of the medium oscillate in the direction of wave propagation - in all elastic media;

x

oscillation direction

points of the environment

transverse - particles of the medium oscillate perpendicular to the direction of wave propagation - on the surface of the liquid.

X

Types of mechanical waves:

elastic waves - propagation of elastic deformations;

waves on the surface of a liquid.

Wave characteristics:

Let A oscillate according to the law:
.

Then B oscillates with a delay by an angle
, where
, i.e.

Wave energy.

is the total energy of one particle. If particlesN, then where - epsilon, V - volume.

Epsilon– energy per unit volume of the wave – volumetric energy density.

The wave energy flux is equal to the ratio of the energy transferred by waves through a certain surface to the time during which this transfer is carried out:
, watt; 1 watt = 1J/s.

Energy Flux Density - Wave Intensity- energy flow through a unit area - a value equal to the average energy transferred by a wave per unit time per unit area of ​​the cross section.

[W/m2]

.

Umov vector– vector I showing the direction of wave propagation and equal to the flow wave energy passing through a unit area perpendicular to this direction:

.

Physical characteristics of the wave:

Vibrational:

1. amplitude

Wave:

1. wavelength

   wave speed

   intensity

Complex oscillations (relaxation) - different from sinusoidal.

Fourier transform- any complex periodic function can be represented as the sum of several simple (harmonic) functions, the periods of which are multiples of the period of the complex function - this is harmonic analysis. Occurs in parsers. The result is the harmonic spectrum of a complex oscillation:

BUT

0

Sound - vibrations and waves that act on the human ear and cause an auditory sensation.

Sound vibrations and waves are a special case of mechanical vibrations and waves. Types of sounds:

tones- sound, which is a periodic process:

1. simple - harmonic - tuning fork

   complex - anharmonic - speech, music

A complex tone can be decomposed into simple ones. The lowest frequency of such decomposition is the fundamental tone, the remaining harmonics (overtones) have frequencies equal to 2 other. A set of frequencies indicating their relative intensity is the acoustic spectrum.

Noise - sound with a complex non-repeating time dependence (rustle, creak, applause). The spectrum is continuous.

Physical characteristics of sound:

Hearing sensation characteristics:

Height is determined by the frequency of the sound wave. The higher the frequency, the higher the tone. The sound of greater intensity is lower.

Timbre– determined by the acoustic spectrum. The more tones, the richer the spectrum.

Volume- characterizes the level of auditory sensation. Depends on sound intensity and frequency. Psychophysical Weber-Fechner law: if you increase irritation in geometric progression(in the same number of times), then the feeling of this irritation will increase in arithmetic progression(by the same amount).

, where E is loudness (measured in phons);
- intensity level (measured in bels). 1 bel - change in intensity level, which corresponds to a change in sound intensity by 10 times. K - proportionality coefficient, depends on frequency and intensity.

The relationship between loudness and intensity of sound is equal loudness curves, built on experimental data (they create a sound with a frequency of 1 kHz, change the intensity until an auditory sensation arises similar to the sensation of the volume of the sound under study). Knowing the intensity and frequency, you can find the background.

Audiometry- a method for measuring hearing acuity. The instrument is an audiometer. The resulting curve is an audiogram. The threshold of hearing sensation at different frequencies is determined and compared.

Noise meter - noise level measurement.

In the clinic: auscultation - stethoscope / phonendoscope. A phonendoscope is a hollow capsule with a membrane and rubber tubes.

Phonocardiography - graphic registration of backgrounds and heart murmurs.

Percussion.

Ultrasound– mechanical vibrations and waves with a frequency above 20 kHz up to 20 MHz. Ultrasound emitters are electromechanical emitters based on the piezoelectric effect ( alternating current to the electrodes, between which - quartz).

The wavelength of ultrasound is less than the wavelength of sound: 1.4 m - sound in water (1 kHz), 1.4 mm - ultrasound in water (1 MHz). Ultrasound is well reflected at the border of the bone-periosteum-muscle. Ultrasound will not penetrate into the human body if it is not lubricated with oil (air layer). The speed of propagation of ultrasound depends on the environment. Physical processes: microvibrations, destruction of biomacromolecules, restructuring and damage of biological membranes, thermal effect, destruction of cells and microorganisms, cavitation. In the clinic: diagnostics (encephalograph, cardiograph, ultrasound), physiotherapy (800 kHz), ultrasonic scalpel, pharmaceutical industry, osteosynthesis, sterilization.

infrasound– waves with a frequency less than 20 Hz. Adverse action - resonance in the body.

vibrations. Beneficial and harmful action. Massage. vibration disease.

Doppler effect– change in the frequency of the waves perceived by the observer (wave receiver) due to the relative motion of the wave source and the observer.

Case 1: N approaches I.

Case 2: And approaches N.

Case 3: approach and distance of I and H from each other:

System: ultrasonic generator - receiver - is motionless relative to the medium. The object is moving. It receives ultrasound with a frequency
, reflects it, sending it to the receiver, which receives an ultrasonic wave with a frequency
. Frequency difference - doppler frequency shift:
. It is used to determine the speed of blood flow, the speed of movement of the valves.

Themes USE codifier: mechanical waves, wavelength, sound.

mechanical waves - this is the process of propagation in space of oscillations of particles of an elastic medium (solid, liquid or gaseous).

The presence of elastic properties in a medium is necessary condition wave propagation: the deformation that occurs in any place, due to the interaction of neighboring particles, is successively transferred from one point of the medium to another. different types deformations will correspond to different types of waves.

Longitudinal and transverse waves.

The wave is called longitudinal, if the particles of the medium oscillate parallel to the direction of wave propagation. A longitudinal wave consists of alternating tensile and compressive strains. On fig. 1 shows a longitudinal wave, which is an oscillation of flat layers of the medium; the direction along which the layers oscillate coincides with the direction of wave propagation (i.e., perpendicular to the layers).

A wave is called transverse if the particles of the medium oscillate perpendicular to the direction of wave propagation. A transverse wave is caused by shear deformations of one layer of the medium relative to another. On fig. 2, each layer oscillates along itself, and the wave travels perpendicular to the layers.

Longitudinal waves can propagate in solids, liquids and gases: in all these media, an elastic reaction to compression occurs, as a result of which there will be compression and rarefaction running one after another.

However, liquids and gases, unlike solids, do not have elasticity with respect to the shear of the layers. Therefore, transverse waves can propagate in solids, but not inside liquids and gases*.

It is important to note that during the passage of the wave, the particles of the medium oscillate near constant equilibrium positions, i.e., on average, remain in their places. The wave thus
transfer of energy without transfer of matter.

The easiest to learn harmonic waves. They are caused by an external influence on the environment, changing according to the harmonic law. When a harmonic wave propagates, the particles of the medium make harmonic vibrations with a frequency equal to the frequency of the external influence. In the future, we will restrict ourselves to harmonic waves.

Let us consider the process of wave propagation in more detail. Let us assume that some particle of the medium (particle ) began to oscillate with a period . Acting on a neighboring particle, it will pull it along with it. The particle, in turn, will pull the particle along with it, etc. Thus, a wave will arise in which all particles will oscillate with a period.

However, particles have mass, i.e., they have inertia. It takes some time to change their speed. Consequently, the particle in its motion will lag somewhat behind the particle , the particle will lag behind the particle, etc. When the particle finishes the first oscillation after some time and starts the second, the particle , located at a certain distance from the particle, will start its first oscillation.

So, for a time equal to the period of particle oscillations, the perturbation of the medium propagates over a distance . This distance is called wavelength. The oscillations of the particle will be identical to the oscillations of the particle, the oscillations of the next particle will be identical to the oscillations of the particle, etc. The oscillations, as it were, reproduce themselves at a distance can be called spatial oscillation period; along with the time period, it is the most important characteristic of the wave process. In a longitudinal wave, the wavelength is equal to the distance between adjacent compressions or rarefactions (Fig. 1). In the transverse - the distance between adjacent humps or depressions (Fig. 2). In general, the wavelength is equal to the distance (along the direction of wave propagation) between two nearest particles of the medium that oscillate in the same way (i.e., with a phase difference equal to ).

Wave propagation speed is the ratio of the wavelength to the period of oscillation of the particles of the medium:

The frequency of the wave is the frequency of particle oscillations:

From here we get the relationship of the wave speed, wavelength and frequency:

. (1)

Sound.

sound waves in broad sense are any waves propagating in an elastic medium. In a narrow sense sound called sound waves in the frequency range from 16 Hz to 20 kHz, perceived by the human ear. Below this range is the area infrasound, above - area ultrasound.

The main characteristics of sound are volume and height.
The loudness of sound is determined by the amplitude of pressure fluctuations in the sound wave and is measured in special units - decibels(dB). So, the volume of 0 dB is the threshold of audibility, 10 dB is the ticking of a clock, 50 dB is a normal conversation, 80 dB is a scream, 130 dB is the upper limit of audibility (the so-called pain threshold).

Tone - this is the sound that a body makes, making harmonic vibrations (for example, a tuning fork or a string). The pitch is determined by the frequency of these oscillations: the higher the frequency, the higher the sound seems to us. So, by pulling the string, we increase the frequency of its oscillations and, accordingly, the pitch.

The speed of sound in different media is different: the more elastic the medium is, the faster sound propagates in it. In liquids, the speed of sound is greater than in gases, and in solids it is greater than in liquids.
For example, the speed of sound in air at is approximately 340 m / s (it is convenient to remember it as "a third of a kilometer per second") *. In water, sound propagates at a speed of about 1500 m/s, and in steel - about 5000 m/s.
notice, that frequency sound from a given source in all media is the same: the particles of the medium make forced oscillations with the frequency of the sound source. According to formula (1), we then conclude that when passing from one medium to another, along with the speed of sound, the length of the sound wave changes.

mechanical waves

If oscillations of particles are excited in any place of a solid, liquid or gaseous medium, then due to the interaction of atoms and molecules of the medium, oscillations begin to be transmitted from one point to another with a finite speed. The process of propagation of oscillations in a medium is called wave .

mechanical waves there are different types. If in a wave the particles of the medium experience a displacement in a direction perpendicular to the direction of propagation, then the wave is called transverse . An example of a wave of this kind can be waves running along a stretched rubber band (Fig. 2.6.1) or along a string.

If the displacement of the particles of the medium occurs in the direction of wave propagation, then the wave is called longitudinal . Waves in an elastic rod (Fig. 2.6.2) or sound waves in a gas are examples of such waves.

Waves on the liquid surface have both transverse and longitudinal components.

Both in transverse and longitudinal waves, there is no transfer of matter in the direction of wave propagation. In the process of propagation, the particles of the medium only oscillate around the equilibrium positions. However, waves carry the energy of oscillations from one point of the medium to another.

characteristic feature mechanical waves is that they propagate in material media (solid, liquid or gaseous). There are waves that can also propagate in a vacuum (for example, light waves). For mechanical waves, a medium is required that has the ability to store kinetic and potential energy. Therefore, the environment must have inert and elastic properties. In real environments, these properties are distributed throughout the volume. So, for example, any small element of a solid body has mass and elasticity. In the simplest one-dimensional model a solid body can be represented as a collection of balls and springs (Fig. 2.6.3).

Longitudinal mechanical waves can propagate in any media - solid, liquid and gaseous.

If in a one-dimensional model of a rigid body one or more balls are displaced in a direction perpendicular to the chain, then a deformation will occur shear. The springs deformed under such a displacement will tend to return the displaced particles to the equilibrium position. In this case, elastic forces will act on the nearest undisplaced particles, tending to deflect them from the equilibrium position. As a result, a transverse wave will run along the chain.

In liquids and gases, elastic shear deformation does not occur. If one layer of liquid or gas is displaced by some distance relative to the neighboring layer, then no tangential forces will appear at the boundary between the layers. The forces acting on the boundary of a liquid and a solid, as well as the forces between adjacent layers of a fluid, are always directed along the normal to the boundary - these are pressure forces. The same applies to gaseous media. Hence, transverse waves cannot exist in liquid or gaseous media.

Of considerable interest for practice are simple harmonic or sine waves . They are characterized amplitudeA particle vibrations, frequencyf and wavelengthλ. Sinusoidal waves propagate in homogeneous media with some constant speed υ.

Bias y (x, t) particles of the medium from the equilibrium position in a sinusoidal wave depends on the coordinate x on axle OX, along which the wave propagates, and from time t according to law.

In the 7th grade physics course, you studied mechanical vibrations. It often happens that, having arisen in one place, vibrations propagate to neighboring regions of space. Recall, for example, the propagation of vibrations from a pebble thrown into the water or the vibrations of the earth's crust propagating from the epicenter of an earthquake. In such cases, they speak of wave motion - waves (Fig. 17.1). In this section, you will learn about the features of wave motion.

Create mechanical waves

Let's get pretty long rope, one end of which is attached to vertical surface, and we will move the second one up and down (oscillate). Vibrations from the hand will spread along the rope, gradually involving oscillating motion more and more distant points - a mechanical wave will run along the rope (Fig. 17.2).

A mechanical wave is the propagation of oscillations in an elastic medium*.

Now we fix a long soft spring horizontally and apply a series of successive blows to its free end - a wave will run in the spring, consisting of condensations and rarefaction of the coils of the spring (Fig. 17.3).

The waves described above can be seen, but most mechanical waves are invisible, such as sound waves (Figure 17.4).

At first glance, all mechanical waves are completely different, but the reasons for their occurrence and propagation are the same.

We find out how and why a mechanical wave propagates in a medium

Any mechanical wave is created by an oscillating body - the source of the wave. Performing an oscillatory motion, the wave source deforms the layers of the medium closest to it (compresses and stretches them or displaces them). As a result, elastic forces arise that act on neighboring layers of the medium and force them to carry out forced oscillations. These layers, in turn, deform the next layers and cause them to oscillate. Gradually, one by one, all layers of the medium are involved in oscillatory motion - a mechanical wave propagates in the medium.

Rice. 17.6. In a longitudinal wave, the layers of the medium oscillate along the direction of wave propagation

Distinguish between transverse and longitudinal mechanical waves

Let's compare wave propagation along a rope (see Fig. 17.2) and in a spring (see Fig. 17.3).

Separate parts of the rope move (oscillate) perpendicular to the direction of wave propagation (in Fig. 17.2, the wave propagates from right to left, and parts of the rope move up and down). Such waves are called transverse (Fig. 17.5). During the propagation of transverse waves, some layers of the medium are displaced relative to others. Displacement deformation is accompanied by the appearance of elastic forces only in solids, so transverse waves cannot propagate in liquids and gases. So, transverse waves propagate only in solids.

When a wave propagates in a spring, the coils of the spring move (oscillate) along the direction of wave propagation. Such waves are called longitudinal (Fig. 17.6). When a longitudinal wave propagates, compressive and tensile deformations occur in the medium (along the direction of wave propagation, the density of the medium either increases or decreases). Such deformations in any medium are accompanied by the appearance of elastic forces. Therefore, longitudinal waves propagate in solids, and in liquids, and in gases.

Waves on the surface of a liquid are neither longitudinal nor transverse. They have a complex longitudinal-transverse character, while the liquid particles move along ellipses. This is easy to verify if you throw a light chip into the sea and watch its movement on the surface of the water.

Finding out the basic properties of waves

1. Oscillatory motion from one point of the medium to another is not transmitted instantly, but with some delay, so the waves propagate in the medium with a finite speed.

2. The source of mechanical waves is an oscillating body. When a wave propagates, the vibrations of parts of the medium are forced, so the frequency of vibrations of each part of the medium is equal to the frequency of vibrations of the wave source.

3. Mechanical waves cannot propagate in a vacuum.

4. Wave motion is not accompanied by the transfer of matter - parts of the medium only oscillate about the equilibrium positions.

5. With the arrival of the wave, parts of the medium begin to move (acquire kinetic energy). This means that when the wave propagates, energy is transferred.

Transfer of energy without transfer of matter - the most important property any wave.

Remember the propagation of waves on the surface of the water (Fig. 17.7). What observations confirm the basic properties of wave motion?

We remember physical quantities characterizing fluctuations

A wave is the propagation of oscillations, so the physical quantities that characterize oscillations (frequency, period, amplitude) also characterize the wave. So, let's remember the material of the 7th grade:

	Physical quantities characterizing oscillations
	Oscillation frequency ν	Oscillation period T	Oscillation amplitude A
Define	number of oscillations per unit of time	time of one oscillation	the maximum distance a point deviates from its equilibrium position
Formula to determine
	N is the number of oscillations per time interval t
Unit in SI		second (s)

Note! When a mechanical wave propagates, all parts of the medium in which the wave propagates oscillate with the same frequency (ν), which is equal to the oscillation frequency of the wave source, so the period

oscillations (T) for all points of the medium is also the same, because

But the amplitude of oscillations gradually decreases with distance from the source of the wave.

We find out the length and speed of propagation of the wave

Remember the propagation of a wave along a rope. Let the end of the rope carry out one complete oscillation, that is, the propagation time of the wave is equal to one period (t = T). During this time, the wave propagated over a certain distance λ (Fig. 17.8, a). This distance is called the wavelength.

The wavelength λ is the distance over which the wave propagates in a time equal to the period T:

where v is the speed of wave propagation. The unit of wavelength in SI is the meter:

It is easy to see that the points of the rope, located at a distance of one wavelength from each other, oscillate synchronously - they have the same phase of oscillation (Fig. 17.8, b, c). For example, points A and B of the rope move up at the same time, reach the crest of a wave at the same time, then start moving down at the same time, and so on.

Rice. 17.8. The wavelength is equal to the distance that the wave propagates during one oscillation (this is also the distance between the two nearest crests or the two nearest troughs)

Using the formula λ = vT, we can determine the propagation velocity

we obtain the formula for the relationship between the length, frequency and speed of wave propagation - the wave formula:

If a wave passes from one medium to another, its propagation speed changes, but the frequency remains the same, since the frequency is determined by the source of the wave. Thus, according to the formula v = λν, when a wave passes from one medium to another, the wavelength changes.

Wave formula

Learning to solve problems

Task. The transverse wave propagates along the cord at a speed of 3 m/s. On fig. 1 shows the position of the cord at some point in time and the direction of wave propagation. Assuming that the side of the cage is 15 cm, determine:

1) amplitude, period, frequency and wavelength;

Analysis of a physical problem, solution

The wave is transverse, so the points of the cord oscillate perpendicular to the direction of wave propagation (they move up and down relative to some equilibrium positions).

1) From fig. 1 we see that the maximum deviation from the equilibrium position (amplitude A of the wave) is equal to 2 cells. So A \u003d 2 15 cm \u003d 30 cm.

The distance between the crest and trough is 60 cm (4 cells), respectively, the distance between the two nearest crests (wavelength) is twice as large. So, λ = 2 60 cm = 120 cm = 1.2m.

We find the frequency ν and the period T of the wave using the wave formula:

2) To find out the direction of movement of the points of the cord, we perform an additional construction. Let the wave move over a small distance over a short time interval Δt. Since the wave shifts to the right, and its shape does not change with time, the pinch points will take the position shown in Fig. 2 dotted.

The wave is transverse, that is, the points of the cord move perpendicular to the direction of wave propagation. From fig. 2 we see that point K after a time interval Δt will be below its initial position, therefore, its speed is directed downwards; point B will move higher, therefore, the speed of its movement is directed upwards; point C will move lower, therefore, the speed of its movement is directed downward.

Answer: A = 30 cm; T = 0.4 s; ν = 2.5 Hz; λ = 1.2 m; K and C - down, B - up.

Summing up

The propagation of oscillations in an elastic medium is called a mechanical wave. A mechanical wave in which parts of the medium oscillate perpendicular to the direction of wave propagation is called transverse; a wave in which parts of the medium oscillate along the direction of wave propagation is called longitudinal.

The wave propagates in space not instantly, but with a certain speed. When a wave propagates, energy is transferred without transfer of matter. The distance over which the wave propagates in a time equal to the period is called the wavelength - this is the distance between the two nearest points that oscillate synchronously (have the same phase of oscillation). The length λ, frequency ν and velocity v of wave propagation are related by the wave formula: v = λν.

test questions

1. Define a mechanical wave. 2. Describe the mechanism of formation and propagation of a mechanical wave. 3. Name the main properties of wave motion. 4. What waves are called longitudinal? transverse? In what environments do they spread? 5. What is the wavelength? How is it defined? 6. How are the length, frequency and speed of wave propagation related?

Exercise number 17

1. Determine the length of each wave in fig. one.

2. In the ocean, the wavelength reaches 270 m, and its period is 13.5 s. Determine the propagation speed of such a wave.

3. Do the speed of wave propagation and the speed of movement of the points of the medium in which the wave propagates coincide?

4. Why does a mechanical wave not propagate in a vacuum?

5. As a result of the explosion produced by geologists, in earth's crust the wave propagated at a speed of 4.5 km/s. Reflected from the deep layers of the Earth, the wave was recorded on the Earth's surface 20 s after the explosion. At what depth does the rock lie, the density of which differs sharply from the density of the earth's crust?

6. In fig. 2 shows two ropes along which a transverse wave propagates. Each rope shows the direction of oscillation of one of its points. Determine the directions of wave propagation.

7. In fig. 3 shows the position of two filaments along which the wave propagates, showing the direction of propagation of each wave. For each case a and b determine: 1) amplitude, period, wavelength; 2) the direction in which this moment time points A, B and C of the cord move; 3) the number of oscillations that any point of the cord makes in 30 s. Consider that the side of the cage is 20 cm.

8. A man standing on the seashore determined that the distance between adjacent wave crests is 15 m. In addition, he calculated that 16 wave crests reach the shore in 75 seconds. Determine the speed of wave propagation.

This is textbook material.

A mechanical or elastic wave is the process of propagation of oscillations in an elastic medium. For example, air begins to oscillate around a vibrating string or speaker cone - the string or speaker has become sources of a sound wave.

For the occurrence of a mechanical wave, two conditions must be met - the presence of a wave source (it can be any oscillating body) and an elastic medium (gas, liquid, solid).

Find out the cause of the wave. Why do the particles of the medium surrounding any oscillating body also come into oscillatory motion?

The simplest model of a one-dimensional elastic medium is a chain of balls connected by springs. Balls are models of molecules, the springs connecting them model the forces of interaction between molecules.

Suppose the first ball oscillates with a frequency ω. Spring 1-2 is deformed, an elastic force arises in it, which changes with frequency ω. Under the action of an external periodically changing force, the second ball begins to perform forced oscillations. Since forced oscillations always occur at the frequency of the external driving force, the oscillation frequency of the second ball will coincide with the oscillation frequency of the first. However, the forced oscillations of the second ball will occur with some phase delay relative to the external driving force. In other words, the second ball will begin to oscillate somewhat later than the first ball.

The vibrations of the second ball will cause a periodically changing deformation of the spring 2-3, which will make the third ball oscillate, and so on. Thus, all the balls in the chain will alternately be involved in an oscillatory motion with the oscillation frequency of the first ball.

Obviously, the cause of wave propagation in an elastic medium is the presence of interaction between molecules. The oscillation frequency of all particles in the wave is the same and coincides with the oscillation frequency of the wave source.

According to the nature of particle oscillations in a wave, waves are divided into transverse, longitudinal and surface waves.

AT longitudinal wave particles oscillate along the direction of wave propagation.

The propagation of a longitudinal wave is associated with the occurrence of tensile-compressive deformation in the medium. In the stretched areas of the medium, a decrease in the density of the substance is observed - rarefaction. In compressed areas of the medium, on the contrary, there is an increase in the density of the substance - the so-called thickening. For this reason, a longitudinal wave is a movement in space of areas of condensation and rarefaction.

Tensile-compressive deformation can occur in any elastic medium, so longitudinal waves can propagate in gases, liquids and solids. An example of a longitudinal wave is sound.

AT shear wave particles oscillate perpendicular to the direction of wave propagation.

Spreading shear wave associated with the occurrence of shear deformation in the medium. This type of deformation can only exist in solids, so transverse waves can only propagate in solids. An example of a shear wave is the seismic S-wave.

surface waves occur at the interface between two media. Oscillating particles of the medium have both transverse, perpendicular to the surface, and longitudinal components of the displacement vector. During their oscillations, the particles of the medium describe elliptical trajectories in a plane perpendicular to the surface and passing through the direction of wave propagation. An example of surface waves are waves on the water surface and seismic L - waves.

The wave front is the locus of points reached by wave process. The shape of the wave front can be different. The most common are plane, spherical and cylindrical waves.

Note that the wavefront is always located perpendicular direction of the wave! All points of the wavefront will begin to oscillate in one phase.

To characterize the wave process, the following quantities are introduced:

1. Wave frequencyν is the oscillation frequency of all the particles in the wave.

2. Wave amplitude A is the oscillation amplitude of the particles in the wave.

3. Wave speedυ is the distance over which the wave process (perturbation) propagates per unit time.

Please note that the speed of the wave and the speed of oscillation of the particles in the wave are different concepts! The speed of a wave depends on two factors: the type of wave and the medium in which the wave propagates.

The general pattern is as follows: the speed of a longitudinal wave in a solid is greater than in liquids, and the speed in liquids, in turn, is greater than the speed of a wave in gases.

It is not difficult to understand the physical reason for this regularity. The cause of wave propagation is the interaction of molecules. Naturally, the perturbation propagates faster in the medium where the interaction of molecules is stronger.

In the same medium, the regularity is different - the speed of the longitudinal wave is greater than the speed of the transverse wave.

For example, the speed of a longitudinal wave in a solid, where E is the elastic modulus (Young's modulus) of the substance, ρ is the density of the substance.

Shear wave velocity in a solid, where N is the shear modulus. Since for all substances , then . One of the methods for determining the distance to the source of an earthquake is based on the difference in the velocities of longitudinal and transverse seismic waves.

The speed of a transverse wave in a stretched cord or string is determined by the tension force F and the mass per unit length μ:

4. Wavelength λ - minimum distance between points that oscillate equally.

For waves traveling on the surface of water, the wavelength is easily defined as the distance between two adjacent humps or adjacent depressions.

For a longitudinal wave, the wavelength can be found as the distance between two adjacent concentrations or rarefactions.

5. In the process of wave propagation, sections of the medium are involved in an oscillatory process. An oscillating medium, firstly, moves, therefore, it has kinetic energy. Secondly, the medium through which the wave runs is deformed, therefore, it has potential energy. It is easy to see that wave propagation is associated with the transfer of energy to unexcited parts of the medium. To characterize the energy transfer process, we introduce wave intensity I.