Wave Motion

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Wave Motion

A wave is a disturbance that moves from place to place in a medium, carrying energy with it. The behavior of waves is closely related to the concept of oscillations, which will be discussed first.

A good example of an oscillation is that of an object attached to the end of a spring hanging from a fixed clamp. When the object is at rest, the spring is stretched so that its upward pull balances the weight of the object. This is the equilibrium position. If the object is lifted a short distance above the equilibrium position and released, it will fall until the force of the spring stops it and pulls it back upward through the equilibrium position and nearly to the point where it was lifted. Then it will fall again and spring upward again, etc. The energy in the oscillating motion came from the original disturbance, which in this case moved the object to a position above the equilibrium point. At that position, the object was at its maximum displacement. The distance between the equilibrium point and the maximum displacement is the amplitude. The larger the amplitude, the greater the energy in the motion.

Consider a duplicate and identical object-spring system hung side-by-side with the first one, but without the two being in contact in any way. If the first object is disturbed, it oscillates just as before and the second object remains stationary at its equilibrium position. However, the situation becomes different when the two objects are connected with a rubber band and then only the first object is disturbed. It begins to oscillate as before, but soon the second object starts to oscillate also. The rubber band allows energy to transfer to the second object, which will eventually move with the same frequency as the first oscillation. We can make the experiment more complicated if we use a large number of springs hanging in a row, with each object

connected to the one before and after it with rubber bands. If only the first object is disturbed, the oscillation will pass its energy through all the springs. After the energy has been transferred to the next few springs, the first spring will become still with its object back at its equilibrium point. This shows exactly how a disturbance can move as a wave through a medium. In this example, the medium is composed of the objects on springs, which act as coupled oscillators.

The way that a disturbance is transferred from one part of a medium to another in the spring model is very similar to the way that waves move in water, air, or a guitar string. Water is composed of a great number of H₂O molecules lying very close to each other. If the water has been undisturbed for a long time, its surface will be calm and the molecules will be relatively stationary (of course, they are not completely stationary, but their motion is microscopic). Now suppose the water is disturbed by an object impinging on it. This produces a disturbance as many molecules are forced downward. We have all seen a wave move on the surface of the water away from the position of our tap, and this is simply the disturbance being transferred from one molecule to another. The molecules of water all exert an electrical force on their neighbors, which are quite close. This holds them together and provides the same effect as the rubber bands in the example above. Just as before, the larger the original displacement, the greater the energy in the disturbance and the bigger the energy that the wave carries.

The water wave discussed above is an example of a traveling wave since the disturbance moves from place to place in the medium. It can also be classified as a transverse wave because the direction of the disturbance (vertical in this case) is perpendicular to the

KEY TERMS

Frequency —The number of cycles, or repetitions, of an oscillating motion which occur per second.

Medium —A material in which a disturbance (oscillation) at one location can transfer its energy to nearby locations, for example from one molecule of water to another.

Wave train —A repeated pattern of individual waves which are produced with a specific rhythm, or frequency.

direction that the wave travels (horizontally). There are also longitudinal waves, like those that carry the energy of sound in air, in which the direction of the disturbance is the same as that of the wave motion. This is easy to visualize if you have ever seen a speaker move when the volume is turned up very loud. The sudden movements of the speaker compress the nearby air and that disturbance moves in the same direction toward you and your ears.

A repeated pattern of individual waves, a wave train, often occurs in water bodies. A wave train is produced in water by tapping the surface with a specific rhythm, or frequency. A complementary characteristic of a wave train is the wavelength. Suppose the surface of the water is tapped with a specific frequency and a picture of the resulting waves is taken. In effect, this “freezes” the wave train in time. Examination of the picture will show that there is a constant distance between the individual waves; this is the wavelength. The frequency tells how often the wave train repeats itself in time and the inverse of the wavelength tells how often the wave train repeats itself in space. Multiplying the values of the frequency and the wavelength results in the speed at which the wave moves.

Waves have many interesting properties. They can reflect from surfaces and refract, or change their direction, when they pass from one medium into another. These properties are commonly observed in the behavior of light, which behaves as a wave in many everyday circumstances. Light reflects off of shiny surfaces such as mirrors and glass. An example of refraction is the bending of light when it passes from water into air. For this reason, when looking at objects underwater, they appear to be at different locations than their real positions.

Waves can also combine, or interfere. For example, if two waves reach a particular point so that they both disturb the medium in the same way the amplitude of the wave will increase additively. This is constructive interference. Likewise, destructive interference happens when the disturbances of different waves cancel. Interference can also lead to standing waves which appear to be stationary—the medium is still disturbed, but the disturbances are oscillating in place. This occurs within confined regions, like a bathtub or a guitar string (fixed at both ends). For just the right wavelengths, traveling wave trains and their reflections off the boundaries can interfere to produce a wave that appears stationary.

See also Acoustics; Fluid dynamics.