Conditions for the emergence of mechanical waves. Mechanical waves: source, properties, formulas
Topics of the 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 the medium is a necessary condition for the propagation of waves: 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 different types 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 perform harmonic oscillations with a frequency equal to the frequency of the external action. 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 somewhat lag 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 will start its first oscillation, located at a certain distance from the particle.
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 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 a broad sense, any waves propagating in an elastic medium are called. 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.
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.
IN 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 Oh. An example of a longitudinal wave is sound.
IN 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 kind 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 the 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. Wavelengthλ is the 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.
wave process- the process of energy transfer without the transfer of matter.
mechanical wave- perturbation propagating in an elastic medium.
The presence of an elastic medium - necessary condition propagation of mechanical waves.
The transfer of energy and momentum in the medium occurs as a result of the interaction between neighboring particles of the medium.
Waves are longitudinal and transverse.
Longitudinal mechanical wave - a wave in which the movement of particles of the medium occurs in the direction of wave propagation. Transverse mechanical wave - a wave in which the particles of the medium move perpendicular to the direction of wave propagation.
Longitudinal waves can propagate in any medium. Transverse waves do not occur in gases and liquids, since they
there are no fixed positions of particles.
Periodic external action causes periodic waves.
harmonic wave- a wave generated by harmonic vibrations of the particles of the medium.
Wavelength- the distance over which the wave propagates during the period of oscillation of its source:
mechanical wave speed- velocity of perturbation propagation in the medium. Polarization is the ordering of the directions of oscillations of particles in a medium.
Plane of polarization- the plane in which the particles of the medium vibrate in the wave. A linearly polarized mechanical wave is a wave whose particles oscillate along a certain direction (line).
Polarizer- a device that emits a wave of a certain polarization.
standing wave- a wave formed as a result of the superposition of two harmonic waves propagating towards each other and having the same period, amplitude and polarization.
Antinodes of a standing wave- the position of the points with the maximum amplitude of oscillations.
Knots of a standing wave- non-moving points of the wave, the oscillation amplitude of which is equal to zero.
On the length l of a string fixed at the ends, an integer n half-waves of transverse standing waves fit:
Such waves are called oscillation modes.
The oscillation mode for an arbitrary integer n > 1 is called the nth harmonic or the nth overtone. The oscillation mode for n = 1 is called the first harmonic or fundamental oscillation mode. Sound waves are elastic waves in the medium that cause auditory sensations in a person.
The frequency of oscillations corresponding to sound waves lies in the range from 16 Hz to 20 kHz.
The speed of propagation of sound waves is determined by the rate of transfer of interaction between particles. The speed of sound in a solid v p, as a rule, is greater than the speed of sound in a liquid v l, which, in turn, exceeds the speed of sound in a gas v g.
Sound signals are classified by pitch, timbre and loudness. The pitch of the sound is determined by the frequency of the source sound vibrations. The higher the oscillation frequency, the higher the sound; fluctuations of low frequencies correspond to low sounds. The timbre of sound is determined by the form of sound vibrations. The difference in the shape of vibrations having the same period is associated with different relative amplitudes of the fundamental mode and overtone. Sound volume is characterized by the level of sound intensity. Sound intensity - the energy of sound waves incident on an area of 1 m 2 in 1 s.
DEFINITION
Longitudinal wave- this is a wave, during the propagation of which the displacement of the particles of the medium occurs in the direction of the wave propagation (Fig. 1, a).
The cause of the occurrence of a longitudinal wave is compression / extension, i.e. the resistance of a medium to a change in its volume. In liquids or gases, such deformation is accompanied by rarefaction or compaction of the particles of the medium. Longitudinal waves can propagate in any media - solid, liquid and gaseous.
Examples of longitudinal waves are waves in an elastic rod or sound waves in gases.
transverse waves
DEFINITION
transverse wave- this is a wave, during the propagation of which the displacement of the particles of the medium occurs in the direction perpendicular to the propagation of the wave (Fig. 1b).
The cause of a transverse wave is the shear deformation of one layer of the medium relative to another. When a transverse wave propagates in a medium, ridges and troughs are formed. Liquids and gases, unlike solids, do not have elasticity with respect to layer shear, i.e. do not resist shape change. Therefore, transverse waves can propagate only in solids.
Examples of transverse waves are waves traveling along a stretched rope or along a string.
Waves on the surface of a liquid are neither longitudinal nor transverse. If you throw a float on the surface of the water, you can see that it moves, swaying on the waves, in a circular fashion. Thus, a wave on a liquid surface has both transverse and longitudinal components. On the surface of a liquid, waves of a special type can also occur - the so-called surface waves. They arise as a result of the action and force of surface tension.
Examples of problem solving
EXAMPLE 1
| Exercise | Determine the direction of propagation of the transverse wave if the float at some point in time has the direction of velocity indicated in the figure. |
| Solution | Let's make a drawing. Let's draw the surface of the wave near the float after a certain time interval, considering that during this time the float went down, since it was directed down at the moment of time. Continuing the line to the right and to the left, we show the position of the wave at time . Comparing the position of the wave at the initial moment of time (solid line) and at the moment of time (dashed line), we conclude that the wave propagates to the left. |
