Wave graphs
You need to know about two types of graph that can be used to represent waves:
- Displacement-distance graphs.
- Displacement-time graphs.
Displacement-distance
A displacement-distance graph is a snapshot of the wave at one particular time.
The graph can be used to work out the wavelength, \(\lambda\), of the wave.
The wavelength of this wave = 40 cm.
You can also tell from the graph that:
- There are two complete waves.
- The amplitude of the waves = 10 cm.
Displacement-time
A displacement-time graph shows how the displacement of one point on the wave varies over time.
The x-axis of the graph is time, and so it is used to work out the period of the wave.
Example
Calculate the period and frequency of the waves shown in the diagram.
Answer
The time for one complete wave = 0.1 s and so the period, T = 0.1 s.
\(\text{f =}~\frac{\text{1}}{\text{T}}\)
\(\text{f =}~\frac{\text{1}}{\text{0.1}}\)
f = 10 Hz
The frequency of the wave is 10 Hz.
Key points
- If the x-axis is distance, the graph is used to work out wavelength, \(\lambda\).
- If the x-axis is time, the graph is used to work out period, T.
- Both graphs can be used to work out the amplitude of the wave.
Question
A graph of displacement against distance for a wave passing through water is given below.
- What is the wavelength of the wave?
- What is the amplitude of the wave?
Wavelength is the distance covered by one vibration of the wave, usually measured from peak to peak, or trough to trough.
The distance axis is labelled in m, and so the distance between 2 peaks is 8 m.
The wavelength of the wave is 8 m.
Amplitude is the maximum displacement of a point of a wave from its rest position.
The displacement axis is labelled in mm, so the maximum displacement is 2.5 mm.
The amplitude of the wave is 2.5 mm.
