Wave Motion

A wave is nothing more than a disturbance that moves from place to place in some medium, carrying energy with it. Since the behavior of waves is so closely related to the concept of oscillations, that is a good place to start.

There are many examples of simple oscillations, but a very good one is that of an object attached to the end of a spring. Assume that the other end is held fixed, perhaps by a clamp. Suppose the spring hangs vertically and slowly lowers the object until it becomes stationary. The spring is now stretched enough for its upward pull to balance the weight of the object, which at that location is in equilibrium. Now disturb the object by lifting it a short distance above that point and letting go. The object then begins to oscillate vertically as it first falls, until the spring stops it and pulls it back upward to the original position, then it falls 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 instance, the object was at its maximum displacement whose size is the amplitude. The larger the amplitude, the greater the energy in the motion.

If we hang a duplicate object and spring side-by-side with the first one, but without the two being in contact in any way. If we disturb the first object, it oscillates just as before and the second object remains stationary at its equilibrium position. However, the situation becomes different if we connect the two objects with a rubber band and then disturb only the first object. 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 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 demonstrates 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. We can think of the water, perhaps in a bathtub, as being composed of a great number of H₂O molecules lying very close side-by-side. 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 we disturb the water by tapping it with a finger. This produces a disturbance as many molecules are forced downward, the opposite of what happened in our spring example. 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. Just as before, the larger the original displacement, the greater the energy in the disturbance and the bigger the energy that the wave carries. You might ask how the transfer of energy takes place. Actually, the molecules of water all exert some force on their neighbors which are quite close. This holds them together and provides the same effect as the rubber bands.

The wave we just made 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 direction that the wave travels (horizontally). There are also longitudinal waves, Transverse waves produced by a water droplet penetrating the surface of a body of liquid. © Martin Dohrn/Science Photo Library, National Audubon Society Collection/Photo Researchers, Inc. Reproduced with permission.
like those which 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. A wave train can be produced in water by tapping the surface with a specific rhythm, or frequency. A complementary characteristic of a wave train is the wavelength. Suppose a friend taps the water with a specific frequency and you take a picture of the resulting waves. In effect, this lets you "freeze" the wave train in time and examine it. You will notice 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 numerical values of the frequency and the wavelength gives the speed at which the waves move.

Waves have many interesting properties. They can reflect from surfaces and refract, or change their direction, when they pass from one medium into another. If these properties seem familiar, that is because we are accustomed to light behaving in exactly this way. Obviously light reflects, and an example of refraction is the bending of light when it passes from water into air. For this reason, when you look into water, objects appear to be at different locations than their real positions. Light is therefore considered in these instances to behave as though it was a wave produced by moving disturbances of electric and magnetic fields.

Waves can also combine, or interfere. For example, two waves can reach a particular point at just the right time for both to disturb the medium in the same way (such as if two water waves both try to lift the surface at the same time). 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 can only occur 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.