Wave Motion

Wave Motion, in physics, mechanism by which energy is conveyed from one place to another in mechanically propagated waves without the transference of 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 traveling 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 of matter 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 a mass 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 displacement is of electric and magnetic fields of force in space (see Electricity; Electromagnetic Radiation; Electronics; Field).

Waves, such as water or sound waves, are a periodic disturbance of the medium through which they travel. For longitudinal waves, the medium is displaced in the direction of travel. For example, air is compressed and expanded (figure 1) in the same direction that a sound wave travels. For transverse waves, the medium is displaced perpendicular to the direction of travel. Ripples on the surface of a pond are an example of a transverse wave: the water is displaced vertically (figure 2), while the wave itself travels horizontally. Earthquakes generate both P (compression, or longitudinal) and S (shear, or transverse) waves, which travel at different speeds and follow different paths. These differences allow seismologists to estimate where the earthquake occurred. Atomic particles and light can be described by probability waves that, while fundamentally different, behave much like the ripples on a pond.

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 a longitudinal wave (see Fig. 1). The longitudinal wave is always mechanical because it results from successive compressions (state of maximum density and pressure) and rarefactions (state 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 in a taut string that is subjected to a transverse vibration (see Fig. 2); or it may be electromagnetic, such as light, X ray, or radio waves (see Radio; X Ray). Some mechanical wave motions, such as waves on the surface of a liquid, are combinations of both longitudinal and transverse motions, resulting in the circular motion of liquid particles.

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 is called the amplitude of the wave.

The velocity of a wave motion 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 velocity can be doubled by quadrupling the tension, or it can be reduced to one-half by quadrupling the mass of the string. The motion of electromagnetic waves through space is constant at about 300,000 km/sec (about 186,000 mi/sec), or the speed of light. This velocity varies slightly in passage through matter.

This interference pattern was formed by two rods moving rhythmically up and down in a ripple tank. A ripple tank consists of a clear tray of water, an overhead light, and devices to make wave patterns. You can observe a similar pattern by dipping two fingers up and down in a puddle of water or by watching two ducks swim near each other in a lake or pond. The waves from one point source (a rod, finger, duck) interfere with waves from the other point source (another rod, finger, or duck). If two crests arrive at a point together, they superimpose to form a very high crest; if two troughs arrive together, they superimpose to form a very low trough. This is called constructive interference. The bright and dark rings are regions of constructive interference. If a crest from one source arrives at a point at the same instant as a trough from the other source, they cancel each other. This is called destructive interference. The radiating dark rays are regions of destructive interference.

When two waves meet at a point, the resulting displacement of that point will be the sum of the displacements produced by each of the waves. If the displacements are in the same direction, the two waves reinforce each other; if the displacements are in the opposite direction, the waves counteract each other. This phenomenon is known as interference. See also Diffraction.

When two pulses traveling on a string meet each other, the amplitudes of the pulses are added together to produce the shape of the resulting pulse. If the pulses are identical but travel on opposite sides of the string, then the sum of the amplitudes is zero and the string will appear flat for one instant (A). This is called destructive interference. When the two identical pulses travel on the same side of the string, then the sum of the amplitudes is double the amplitude of a single pulse when the pulses are together). This is called constructive interference.

When two waves of equal wavelength and amplitude travel in opposite directions at the same velocity through a medium, stationary, or standing, waves are formed. For example, if one end of a rope is tied to a wall and the other end is shaken up and down, waves will be reflected back along the rope from the wall. Assuming that the reflection is perfectly efficient, the reflected wave will be half a wavelength behind the initiating wave. Interference will take place, and the resultant displacement at any given point and time will be the sum of the individual displacements. No motion will take place at points where the crest of the incident wave meets the trough of the reflected one. Such points are called nodes. Halfway between the nodes, the waves meet in the same phase; that is, crest will coincide with crest and trough with trough. At these points the amplitude of the resultant wave is twice as great as that of the incident wave. Thus, the rope is divided into sections one wavelength long by the nodes, which do not progress along the rope, while the rope between the nodes vibrates transversely.

A wave pulse on a string is generated by a quick movement of a hand and travels down the string toward the left (A). If the end of the string is free to move up and down at the wall, the pulse will come back down the string on the same side (C1). If the string is tied to the wall, the pulse will travel back along the string on the opposite side (C2). For the free end, the pulse will have twice the original amplitude at the turnaround point (B1); for the fixed end, the pulse will have no amplitude at the turnaround point (B2).

Stationary waves are present in the vibrating strings of musical instruments. A violin string, for instance, when bowed or plucked, vibrates as a whole, with nodes at the ends, and also vibrates in halves, with a node at the center, in thirds, with two equally spaced nodes, and in various other fractions, all simultaneously. The vibration as a whole produces the fundamental tone, and the other vibrations produce the various harmonics.

In quantum mechanics , the structure of the atom is explained by analogy to a system of standing waves. Much of the development of modern physics is based on the elaboration of the theory of waves and wave motion.