Basic Waves Theory

What are waves?

Waves transfer energy from one point to another without transferring matter. They consist of disturbances which transfer the energy in the direction the wave travels without transferring matter.

There are two types of waves:

• Transverse waves
• Longitudinal waves

Transverse Waves

Transverse waves are wave in which the vibrations of the particles or medium in which the wave travels are at right angles to the direction in which the wave travels.

Water waves are an example of transverse waves. These can be observed in a ripple tank. The animation below shows transverse waves created in a ripple tank.

From the above animation it can be seen that the rubber duck only moves up and down whilst the energy of the wave moves along the tank. Thus the water only move up and down or in other words at right angles to the direction of travel of the wave. The energy however is passed along the water from one wave to the other.

The diagram above gives a side view of transverse water wave. Transverse waves consist of high parts or peaks called crests and low parts called troughs.

The distance between two successive crests or two successive troughs is the wavelength for a transverse wave.

The height of the crest from the undisturbed water position or the depth of the trough from the undisturbed water position is the amplitude of the wave.

Longitudinal Waves

Longitudinal waves are wave in which the vibrations of the particles or medium in which the wave travels are in the same direction as to that in which the wave travels.

Sound waves are an example of longitudinal waves.

The animation above shows sound waves travelling through air. Energy is passed along the air molecules by the lengthways vibration of the air molecules. Thus the air molecules only move to and fro or forwards and backwards in the direction of travel of the wave. The sound energy is transferred from one molecule to another and so travels along the wave.

Amplitude and Wavelength – Longitudinal Waves

The diagram above shows the side view of a sound wave. A sound wave is a longitudinal wave. It is made up of regions where the air molecules are close together and have a higher particle density known as compressions and of regions where the air molecules are farther apart and have a low particle density called rarefactions. In a sound wave the region of compression is at a slightly higher pressure due to the air molecules being pushed together whereas the region of rarefaction is at a slightly lower pressure as the air molecules are farther apart.

The wavelength of a longitudinal wave is the distance between successive compressions or the distance between successive rarefactions.

The amplitude is the maximum distance the vibrating particle travels from its undisturbed distance.

Frequency of Waves

The frequency of a wave is a measure of the number of waves made by a source each second, or the number of waves that pass through a particular point in the medium each second. Frequency is measured in units called Hertz (Hz) which is the number of number of wave cycles per second.

The Wave Equation

This is the equation which relates wave speed, frequency and wavelength.

The animation above shows us that the speed of a wave does not depend on the frequency or the wavelength. As the frequency increases the wavelength decrease so from the wave equation it can be determined that the overall wave speed will remain the same.