Mechanical waves: source, properties, formulas

To imagine what mechanical waves are, you can throw a stone into the water. Circles that arise on it and are alternating depressions and ridges are an example of mechanical waves. What is their essence? Mechanical waves are the process of propagation of vibrations in elastic media.

Waves on the surfaces of liquids

Such mechanical waves exist due to the action of intermolecular interaction forces and gravity on the fluid particles. People have long been studying this phenomenon. The most noteworthy are ocean and sea waves. As the wind speed increases, they change, and their height increases. The shape of the waves also becomes more complicated. In the ocean, they can reach frightening proportions. One of the most striking examples of power are the tsunami that sweeps everything in its path.

Energy of sea and ocean waves

Reaching the shore, the sea waves with a sharp change in depth increase. They sometimes reach a height of several meters. At such moments, the kinetic energy of a colossal mass of water is transferred to coastal obstacles, which under its influence quickly collapse. The power of the surf sometimes reaches grandiose values.

Elastic waves

In mechanics, not only vibrations on the surface of a liquid are studied, but also so-called elastic waves. These are perturbations that propagate in different media 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 rubber tube attached to one end to something. If it is tightened and then a lateral sharp movement creates a disturbance on the second (unsecured) end, you can see how it will "run" through the entire length of the rope to the support and be reflected back.

Source of mechanical waves

The initial perturbation leads to the appearance of a wave in the medium. It is caused by the action of some foreign body, which in physics is called the source of the wave. They can be the hand of a man, who swung a rope, or a stone thrown into the water. In the case where the action of the source is of a transient nature, a single wave often arises in the medium. When the "disturber" makes long oscillatory movements, waves start to appear one after another.

Conditions for the generation of mechanical waves

Such oscillations are not always formed. A necessary condition for their appearance is the appearance, at the time of disturbance of the medium, of the forces that impede it, in particular, the elasticity. They tend to bring the neighboring particles closer together as they diverge, and push them away from each other at the moment of rapprochement. Forces of elasticity, acting on the particles remote from the source of disturbance, begin to remove them from equilibrium. Over time, all particles of the medium are involved in one vibrational motion. The propagation of such oscillations is also a wave.

Mechanical waves in an elastic medium

In an elastic wave, there are two types of motion simultaneously: the oscillations of the particles and the propagation of the perturbation. A longitudinal wave is a mechanical wave whose particles oscillate along the direction of its propagation. A transverse wave is a wave whose medium particles oscillate across the direction of its propagation.

Properties of mechanical waves

Perturbations in the longitudinal wave are rarefactions and compressions, and in the transverse direction - displacements (displacements) of certain layers of the medium with respect to the others. The compression deformation is accompanied by the appearance of elastic forces. In this case, the shear deformation is associated with the appearance of elastic forces exclusively in solids. In gaseous and liquid media, the shear of layers of these media is not accompanied by the appearance of this force. Due to their properties, longitudinal waves are able to propagate in any media, and transverse waves - exclusively in solid.

Features of waves on the surface of liquids

The waves on the surface of the liquid are not longitudinal and not transverse. They have a more complex, so-called longitudinal-transverse character. In this case, the fluid particles move along a circle or along elongated ellipses. Circular motions of particles on the surface of the liquid, and especially with large oscillations, are accompanied by their slow but continuous movement in the direction of wave propagation. It is these properties of mechanical waves in the water that cause the appearance on the shore of various seafood.

Frequency of mechanical waves

If in an elastic medium (liquid, solid, gaseous) to excite the vibration of its particles, then due to the interaction between them it will propagate at a speed u. So, if a vibrating body is in a gaseous or liquid medium, its motion will begin to be transmitted to all 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 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 the oscillations of points in the medium where the wave propagates.

At once it may be unclear how this process takes place. With mechanical waves, the transfer of vibrational energy from its source to the periphery of the medium is associated. In the course of this, there are so-called periodic deformations carried by a wave from one point to another. In this case, the particles of the medium themselves, together with the wave, do not move. They oscillate 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. The mechanical waves have a different frequency. Therefore, they were divided into ranges and created a special scale. The frequency is measured in hertz (Hz).

Basic Formulas

Mechanical waves, whose calculation formulas are fairly simple, are an interesting object for study. The velocity of the wave (υ) is the velocity of its front motion (the geometric locus of all the points to which the oscillation of the medium at the given moment has reached):

Υ = √G / ρ,

Where ρ is the density of the medium, and G is the modulus of elasticity.

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

The wave front is of various kinds, the simplest of which are:

• Spherical - caused by vibrations in a gaseous or liquid medium. The amplitude of the wave in this case decreases as the distance from the source is inversely proportional to the square of the distance.

• Flat - represents a plane that is perpendicular to the direction of wave propagation. It occurs, for example, in a closed piston cylinder, when it makes oscillatory movements. The plane wave is characterized by an almost constant amplitude. Its insignificant decrease when moving away from the disturbance source is related to the degree of viscosity of the gaseous or liquid medium.

Wavelength

The wavelength is understood as the distance to 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 period of the oscillation, υ is the wave velocity, ω is the cyclic frequency, ν is the vibration frequency of the points of the medium.

Since the speed of propagation of a mechanical wave is completely dependent on the properties of the medium, its length λ varies during the transition from one medium to another. In this case, the vibration frequency ν always remains the same. Mechanical and electromagnetic waves are similar in that they transmit energy, but there is no transfer of matter.