Wave properties and the wave equationEdexcel International A Level Physics: Revision notes

A wave transfers energy without transferring matter.

• Amplitude (A): the maximum displacement from the equilibrium position
• Wavelength (λ): the distance between two adjacent points that are in phase, such as adjacent crests
• Period (T): the time for one complete oscillation
• Frequency (f): the number of oscillations per second, in hertz; f = 1/T
• Speed (v): the distance travelled by the wave per second

The wave equation is v = fλ.

Worked example: sound of frequency 680 Hz travels at 340 m s⁻¹, so λ = v/f = 340 / 680 = 0.50 m.

In a transverse wave the oscillations are perpendicular to the direction in which energy travels. Examples are waves on a string, ripples on water and electromagnetic waves.

Each point on a string moves up and down about its equilibrium position, while the wave pattern moves along the string. Crests and troughs are the points of maximum positive and negative displacement.

In a longitudinal wave the oscillations are parallel to the direction of energy travel. Sound in air is an example.

• Molecules oscillate backwards and forwards about fixed equilibrium positions: there is no net flow of air.
• Compressions are regions of high pressure and rarefactions are regions of low pressure.
• The wavelength is the distance between adjacent compressions (or adjacent rarefactions).

The pressure variation is a quarter of a cycle out of phase with the displacement of the molecules.

Two graphs describe a wave:

• Displacement against distance: a snapshot at one instant. It shows the wavelength (between adjacent crests) and the amplitude.
• Displacement against time: the motion of one point. It shows the period (time for one cycle), from which f = 1/T.

For a longitudinal wave the displacement plotted is along the direction of travel (a sign convention for left or right), so the graph looks like that of a transverse wave but does not show the wave's shape.

A stationary (standing) wave has fixed points of zero displacement called nodes and points of maximum amplitude called antinodes; the displacement against distance graph shows this envelope. Adjacent nodes are half a wavelength apart.

Connect a signal generator to a loudspeaker and to one channel of a two-beam oscilloscope. Connect a microphone to the other channel.

1. Set a known frequency f.
2. Move the microphone away from the speaker; the two traces move in and out of phase.
3. Note positions where they are in phase. The distance between adjacent in-phase positions is one wavelength.
4. Measure the distance across many wavelengths (for example 10) with a metre rule and divide, to reduce the percentage uncertainty.
5. Calculate v = fλ; repeat at other frequencies and average, or plot λ against 1/f (gradient = v).