Wave Motion

I

Introduction

Wave Motion, mechanism by which energy is conveyed from one place to another in waves without the transfer of matter. Although matter is not moved from one place to another, many sorts of wave motion can occur only in matter. At any point along the path of transmission a periodic displacement, or oscillation, occurs about a neutral position. The oscillation may be of air molecules, as in the case of sound travelling through the atmosphere; of water molecules, as in waves occurring on the surface of the ocean; or of portions of a rope or a wire spring. In each of these cases the particles oscillate about their own equilibrium position and only the energy moves continuously in one direction. Such waves are called mechanical because the energy is transmitted through a material medium, without an overall movement of the medium itself. The only form of wave motion that requires no material medium for transmission is the electromagnetic wave; in this case the “oscillations” consist of variations in the intensity of electric and magnetic fields (see Electromagnetic Radiation).

II

Types of Waves

Waves are divided into types according to the direction of the displacements in relation to the direction of the motion of the wave itself. If the vibration is parallel to the direction of motion, the wave is known as longitudinal (see Fig. 1). The longitudinal wave is always mechanical because it results from successive compressions (states of maximum density and pressure) and rarefactions (states of minimum density and pressure) of the medium. Sound waves typify this form of wave motion. Another type of wave is the transverse wave, in which the vibrations are at right angles to the direction of motion. A transverse wave may be mechanical, such as the wave projected along a taut string that is subjected to a transverse vibration (see Fig. 2); or it may be electromagnetic, such as light, X-rays, or radio waves. In these cases the directions of the electric and magnetic fields are at right angles to the direction of motion. Some mechanical wave motions, such as waves on the surface of a liquid, are combinations of both longitudinal and transverse motions, resulting in a circular motion of particles of the liquid.

For a transverse wave, the wavelength is the distance between two successive crests or troughs. For longitudinal waves, it is the distance from compression to compression or rarefaction to rarefaction. The frequency of the wave is the number of vibrations per second. The velocity of the wave, which is the speed at which it advances, is equal to the wavelength times the frequency. The maximum displacement involved in the vibration of a mechanical wave is called the amplitude of the wave. In the case of an electromagnetic wave, the amplitude is the maximum strength of the electric or magnetic field.

III

Behaviour of Waves

The velocity of a wave in matter depends on the elasticity and density of the medium. In a transverse wave on a taut string, for example, the velocity depends on the tension of the string and its mass per unit length. The speed can be doubled by quadrupling the tension, or it can be reduced to one-half by quadrupling the mass of the string. The speed of electromagnetic waves is constant at about 300,000 km/s (186,000 mi/s), the speed of light. This velocity varies in passage through matter.

A

Refraction

In general, the alteration in a wave's speed when it moves from one medium to another causes it to change its direction. Thus when a light ray enters glass from air, it slows down to about two-thirds of its speed in air. If it is travelling at an angle to the perpendicular, its direction changes to be closer to the perpendicular. When a ray emerges from glass into air, its speed increases, and the ray is bent away from the perpendicular direction. (A ray travelling in the perpendicular direction, either into the glass or out of it, is not deviated.) This bending of a wave is called refraction.