An Introduction to Waves - Longitudinal and Transverse Waves

5.1 An Introduction to Waves - Longitudinal and Transverse Waves
When you think of a wave, you may not necessarily think of sound waves, or light waves, but instead ocean waves, or even a hand waving. However, even these last two examples are useful in understanding waves. A wave is a periodic disturbance in a medium (or in space). Both the motion of the hand and of the ocean are periodic. The ocean wave is a disturbance of the water, and the hand is a disturbance in space (you could also say that it creates a disturbance in air!).

When considering wave propagation, there are two main kinds of waves, transverse waves, and longitudinal waves. Transverse waves are those in which the wave components (i.e. the individual parts of the medium that is transferring the wave) oscillate in a perpendicular direction to that of the wave motion. Consider a buoy sitting on the surface of the ocean, for example. As a wave goes by, the buoy rises with the crest of the wave, and falls with the trough. It bobs up and down regularly as the waves pass from one side of it to the other, but it doesn’t get carried with the water. The motion of the buoy is in a vertical line, while the water moves horizontally. The crest of a wave is the highest point that it reaches, while the trough of the wave is the lowest point. These are respectively the maximum and minimum amplitudes, or displacement of the wave.
Next, consider a slinky on the floor, held by you and a friend. If you push your end of the slinky towards your friend, and pull it back towards you, a compressed section of slinky will effectively travel down to his end. If you had painted one loop in the slinky red, for example, what would happen to that loop as the compressed section traveled down the slinky? It would move towards your friend as the compression approached that part of the slinky, and away from him when the compression had passed. This kind of wave, where the components oscillate in a parallel direction to the wave motion is called a longitudinal wave. In this case, of course, the components of the medium that transmitted the wave were the loops in the slinky. Sometimes this kind of wave is also called a compressive wave, as it requires pressure on the medium in order to be propagated.
In a longitudinal wave, the crest and trough of a transverse wave correspond respectively to the compression, and the rarefaction. A compression is when the particles in the medium through which the wave is traveling are closer together than in its natural state, that is, when their density is greatest. A rarefaction is when these particles are further apart than is normal, or when their density is least.

Since waves are periodic, the representation of an entire wave can be drawn by simply drawing the activity of one wave component only. One kind of waveform graph is that of the displacement of a single oscillator, or wave component, against time. This can be used for both transverse and longitudinal waves, even though the displacement of each of their components is in different directions. Here is a graph of one such wave.

The amount of time it takes the oscillator to complete one whole cycle is called the time period of a wave, T, and is measured in seconds. Conversely, the reciprocal of this number gives the number of waves that will pass per second. This is called the frequency of a wave, f, and is measured in Hertz, Hz (cycles per second). Finally, the wave’s amplitude, a, is its maximum displacement from its equilibrium position, and is measured in meters.

A wave can also be graphed by taking into account the displacement of all the oscillators in the system at an instance in time. This can be shown on a displacement-distance(from the source) graph, from which we can derive more information about the wave. On this graph, the distance between two similar points on a graph - one cycle- yields new information. In this case, it is called the wavelength, l , and is measured in meters. The product of wavelength and frequency gives the velocity of the wave itself, in meters per second:

Waves that arrive at their crests and troughs at the same time, regardless of any difference in amplitude, are said to be in phase. This term can also be applied to points of a wave that also have this property. Points that are separated by integer multiples of T, or l , are in phase.