Mechanical waves: source, properties, formulas

Imagine what a mechanical wave, you can,throwing a stone into the water. The circles that appear on it and are alternating depressions and ridges are an example of mechanical waves. What is their essence? Mechanical waves - the process of propagation of oscillations in elastic media.

Waves on the surfaces of liquids

Such mechanical waves exist due tothe effects on particles of fluid intermolecular interaction forces and gravity. People have long been studying this phenomenon. Most notable are the ocean and sea waves. As the wind speed increases, they change, and their height increases. The shape of the waves themselves is also complicated. In the ocean, they can reach frightening proportions. One of the most visible examples of power is the tsunami, sweeping away everything in its path.

Energy of sea and ocean waves

Reaching the coast, the sea waves at a sharpchanging depth increase. They sometimes reach a height of several meters. At such moments, the kinetic energy of the colossal mass of water is transmitted to coastal obstacles, which are quickly destroyed under its influence. The power of the surf sometimes reaches grandiose values.

Elastic waves

In mechanics, not only oscillations are studied.the surface of the liquid, but also the so-called elastic waves. These are disturbances that spread in different environments under the action of elastic forces in them. Such a perturbation is any deviation of the particles of a given medium from the equilibrium position. A good example of elastic waves is a long rope or a rubber tube attached at one end to something. If you tighten it tightly and then create a disturbance at the second (loose) end of the lateral sharp movement, you can see how it “runs” along the entire length of the rope to the support and reflects back.

Source of mechanical waves

The initial perturbation results inmedium wave. It is caused by the action of a foreign body, which in physics is called the source of the wave. They can be the hand of a man who has rocked the rope, or a pebble thrown into the water. In the case when the action of the source is of short duration, a single wave often occurs in the medium. When the "troublemaker" makes a long oscillatory motion, the waves begin to occur one after the other.

Conditions for the occurrence of mechanical waves

Such vibrations are not always formed.A necessary condition for their appearance is the occurrence at the moment of perturbation of the medium of the forces hindering it, in particular, of elasticity. They seek to bring together neighboring particles when they diverge, and push them away from each other at the moment of approach. The forces of elasticity, acting on the perturbations of particles distant from the source, begin to bring them out of balance. Over time, all the particles of the medium are involved in one oscillatory motion. The propagation of such oscillations is a wave.

Mechanical waves in an elastic medium

In the elastic wave there are 2 types of movementat the same time: particle oscillations and propagation of a disturbance. A longitudinal wave is called a mechanical wave whose particles oscillate along the direction of its propagation. A transverse wave is a wave whose particles fluctuate across its direction of propagation.

Properties of mechanical waves

Perturbations in the longitudinal wave arerarefaction and compression, and in transverse - shifts (displacements) of some layers of the medium relative to others. The compression deformation is accompanied by the appearance of elastic forces. In this case, shear deformation is associated with the appearance of elastic forces exclusively in solids. In gaseous and liquid media, the shear of the layers of these media is not accompanied by the occurrence of the above-mentioned force. Due to its properties, longitudinal waves are able to propagate in any medium, and transverse - exclusively in solid.

Features of waves on the surface of liquids

Waves on the surface of the liquid are neither longitudinal nortransverse. They have a more complex, so-called longitudinal-transverse character. In this case, the fluid particles move in a circle or in elongated ellipses. The circular movements of particles on the surface of the liquid, and especially with large vibrations, are accompanied by their slow but continuous movement in the direction of wave propagation. It is these properties of mechanical waves in water that cause the appearance of various seafood on the coast.

Frequency of mechanical waves

If in an elastic medium (liquid, solid,gaseous) to excite the oscillation of its particles, then due to the interaction between them, it will propagate at a speed u. So, if an oscillating body is in a gaseous or liquid medium, then its motion will begin to be transmitted to all the particles adjacent to it. They will involve the following in the process and so on. In this case, absolutely all points of the medium will begin to oscillate at the same frequency, equal to the frequency of the oscillating body. It is the frequency of the wave. In other words, this value can be characterized as the frequency of oscillations of points in the medium where the wave propagates.

Immediately it may be unclear howthere is this process. The transfer of vibrational motion energy from its source to the periphery of the medium is associated with mechanical waves. In the course of which there are so-called periodic deformations carried by the wave from one point to another. At the same time, the particles of the medium together with the wave do not move. They hesitate next to their equilibrium position. That is why the propagation of a mechanical wave is not accompanied by the transfer of matter from one place to another. Mechanical waves have a different frequency. Therefore, they were divided into ranges and created a special scale. Frequency is measured in Hertz (Hz).

Basic formulas

Mechanical waves whose formulas are calculatedquite simple, are an interesting object to learn. The speed of a wave (υ) is the speed of movement of its front (the geometrical place of all points to which the oscillation of the medium has reached at the moment):

υ = √G / ρ,

where ρ is the density of the medium, G is the modulus of elasticity.

When calculating, do not confuse the speed of mechanicalwaves in a medium with the speed of movement of the particles of the medium that are involved in the wave process. So, for example, a sound wave in the air propagates with an average speed of oscillation of its molecules at 10 m / s, while the speed of a sound wave in normal conditions is 330 m / s.

Wavefront can be of different types, the simplest of which are:

• Spherical - caused by vibrations in a gaseous or liquid medium. The amplitude of the wave decreases with distance from the source in inverse proportion to the square of the distance.

• Flat - is a plane thatperpendicular to the direction of wave propagation. It occurs, for example, in a closed piston cylinder, when it makes an oscillatory motion. The plane wave is characterized by an almost constant amplitude. Its slight decrease with distance from the source of disturbance is associated with the degree of viscosity of the gaseous or liquid medium.

Wavelength

Under the wavelength we mean the distance by which its front will be moved in a time that equals the period of oscillation of the particles of the medium:

λ = υT = υ / v = 2πυ / ω,

where T is the oscillation period, υ is the wave velocity, ω is the cyclic frequency, ν is the oscillation frequency of medium points.

Since the propagation velocity of mechanicalthe wave is completely dependent on the properties of the medium, then its length λ changes from one medium to another. In this case, the oscillation frequency ν always remains the same. Mechanical and electromagnetic waves are similar in that when they propagate, energy is transferred, but there is no transfer of matter.