# General wave properties

Wave motion

The behaviour of waves affects us every second of our lives. Waves are reaching us constantly: sound waves, light waves, infrared heat, television,  mobile-phone and radio waves, the list goes on. The study of waves is, perhaps, truly the central subject of physics.

There are two types of waves: longitudinal and transverse.

Longitudinal waves: This type of wave can be shown by pushing and pulling a spring. The vibrations of the spring as the wave goes past are backwards and forwards in the direction that the wave is travelling (hence the name ‘longitudinal’). The wave consists of stretched and squashed regions travelling along. The stretching produces regions of rarefaction, while the squashing produces regions of compression. Sound is an example of a longitudinal wave.

Transverse waves: In a transverse wave the vibrations are at right angles to the direction of motion. light, radio and other electromagnetic waves are transverse waves.

In the above examples, the waves are very narrow, and are confined to the spring or the string that they are travelling down. Most waves are not confined in this way. Clearly a single wave on the sea, for example, can be hundreds of metres wide as it moves along.

Wavefront

Water waves are often used to demonstrate the properties of waves because the wavefront of a water wave is easy to see. A wavefront is the moving line that joins all the points on the crest of a wave.

The set of points in space reached by a wave or vibration at the same instant as the wave travels through a medium. Wave fronts generally form a continuous line or surface. The lines formed by crests of ripples on a pond, for example, correspond to curved wave fronts.

What features do all waves have?

The speed a wave travels at depends on the substance or medium it is passing through.

Waves have a repeating shape or pattern.

Waves carry energy without moving material along.

Waves have a wavelength, frequency, amplitude and time period.

The wavelength is the distance between two adjacent peaks or, if you prefer, the distance between two adjacent troughs of the wave. In the case of longitudinal waves, it is the distance between two points of maximum compression, or the distance between two points of minimum compression.

The frequency is the number of peaks (or the number of troughs) that go past each second.

The amplitude is the maximum particle displacement of the medium from the central position. In transverse waves, this is half the crest-to-trough height.

The speed of the wave is simply the speed of the wave as it approaches a ship. The largest ocean wave ever measured accurately had a wavelength of 340 m, a frequency of 0.067 Hz (that is to say one peak every 15 s), and a speed of 23 m/s. The amplitude of the wave was 17 m, so the ship was going 17 m above the level of a smooth sea and then 17 m below. (The waves were 34 m from crest to trough.)

The period (T) is the time taken for each complete cycle of the wave motion. It is closely linked to the frequency (f) by this relationship:

where f- frequency in hertz(Hz), T- period in seconds(s)

The speed of a wave in a given medium is constant. If you change the wavelength, the frequency must change as well. If you imagine that some waves are going past you on a spring or on a rope, then they will be going at a constant speed. If the waves get closer together, then more waves must go past you each second, and that means that the frequency has gone up. The speed, frequency and wavelength of a wave are related by the equation:

where v= wave speed, usually measured in meters/second(m/s)

f= frequency , measured in cycles per second or hertz(Hz)

$lambda$=wavelength , usually measured in meters(m)