If 25 peaks of a wave pass in a second, and if the distance between consecutive peaks of a wave is 4 meters, then how fast is the wave moving?
A section of the wave which passes in a second contains 25 peaks. Every peak is 4 meters from the next. Therefore this 1-second section of the wave is 25 peaks ( 4 meters / peak) = 100 meters long.
The wave thus moves 100 meters in a second, and its velocity is therefore 100 meters/second.
If f peaks/sec pass a given point, and there is distance `lambda meters between peaks, then a wave segment of length f `lambda must pass every second. This means that the velocity is f `lambda meters/second.
In symbols, we use `lambda for wavelength, f for frequency and v for wave velocity and we have
v = f `lambda.
The figure below depicts the f peaks that pass in one second when a wave has frequency f. If the peaks have uniform separation `lambda, then the distance represented is f * `lambda. This distance represents one second's travel for the wave. Therefore the velocity of the wave is v = f * `lambda.
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