Waves are a transfer of energy that can be described as vibrations (or oscillations) about a rest point. Below is a list of key definitions related to waves along with diagrams (sketches of graphs). These diagrams all have displacement on the y-axis but the x-axis can vary from either time or distance.
Rest Position, Crest and Trough
Rest Position – this can also be called the equilibrium position and is the undisturbed position of the particles if they do not vibrate.
Crest (Peak) – a point on a wave at its maximum positive displacement (the highest point of a wave).
Trough – a point on a wave at its maximum negative displacement (the lowest point on a wave).
Displacement and Amplitude
Displacement (x) – the distance a point of a wave has moved from its rest position. The displacement can be positive (above the rest position) or negative (below the rest position). The SI unit for displacement is the metre (m).
Amplitude (A) – the maximum displacement of a point of a wave from its rest position (the rest position to a crest or the rest position to a trough). The SI unit for amplitude is the metre (m).
Wavelength
Wavelength (λ) – the smallest distance between two consecutive, identical points on a wave (i.e. the length of one full cycle of a wave). This could be the distance between two successive crests or two successive troughs. The SI unit for wavelength is the metre (m).
Period and Frequency
Period (T) – the time for a particle to make one full cycle of the wave (this could be measured peak to peak or trough to trough). The SI unit for period is the second (s).
Frequency (f) – the number of oscillations (number of waves passing a fixed point) per unit time. The SI unit for frequency is the Hertz (Hz). Frequency can be calculated using the following equation:
Example
The sketches below show the same wave, the top one against distance and the bottom one against time. From these graphs we can find the amplitude, wavelength and period and also calculate the frequency.
From the definition of amplitude we know it can be found by finding the displacement from the rest position to a crest. If we look at the first crest we can see that the displacement from the rest position is 2m. Therefore, the amplitude is 2m.
We can find the wavelength by finding the distance between two crests. The first peak is at 5m and the second peak is at 25m.The difference (25 – 5) gives us the wavelength. Therefore, the wavelength is 20m.
The period can be calculated in the same way but we need to look at the sketch that shows the wave against time. The first peak is at 2.5s and the second peak is at 12.5s. The difference (12.5 – 2.5) gives us the period. Therefore, the period is 10s.
Now that we have the period we can calculate the frequency by using the equation:
Therefore, the frequency is 0.1Hz.
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