4.2a Travelling waves

Travelling waves (water and string)

You have previously looked at oscillations, and we now extended that into travelling waves. The defining feature of travelling waves is that they transfer energy from one location to another. We will start with basic travelling waves in water and on a string, and then extend in the next section to light and sound waves.

The basics of travelling waves

If an oscillator is connected to a suitable medium (like a piston connected to a string or on the surface of some water) then waves will be created for as long as the oscillator is in motion. As well as concrete physical systems (mechanical waves), we can also have oscillations in things are not so immediately obvious - for example moving electrical charges create oscillations in the electromagnetic (EM) field (electromagnetic waves).

Waves can also be categorised according to how the direction of oscillation relates to the direction in which the energy is travelling. If the medium oscillates in a direction perpendicular to the direction of energy propagation (for example water waves, electromagnetic waves or a wave on a length of string) then it is a transverse wave. If the direction of oscillation is parallel to the direction of travel (such as sound waves or pressure waves) then it is a compression or longitudinal wave. More details will be given on longitudinal waves in the section on sound waves.

Describing waves

Much of the vocabulary we used to describe oscillations is also used to describe travelling waves.

Wavelength: the distance between two points of the same phase, such as the crests of a water waves. Symbol: λ Unit: metre (m)

Period: the time taken for one complete wave to path a point in space. Symbol: T Unit: usually seconds (s)

Frequency: The number of waves that pass a point in space per unit time. Symbol: f Unit: usually hertz (Hz): 1 hertz = 1 wave per second

Displacement: over one wavelength the position of the wave will be vary from the equilibrium position. The amount by which it varies at particular point in space and time is the displacement. Symbol: usually x or s Unit: for mechanical waves usually metres (m).

Amplitude: maximum displacement. Symbol: A or x0, Unit: usually metres (m)

Wave speed

The speed of a wave is the speed of its propagation. It is related to the frequency and wavelength though the equation: c = f λ

You need to know the derivation of this equation. Simply put, speed equals distance divided by time. The length of a wave is a wavelength and the wave will travel a wavelength in a period, so speed = λ / T. Since f = 1 / T, is follows that speed = f λ. The symbol c is traditional for wave speed, but v is used as well. Units: the unit of distance / the unit of time , generally m/s.