Observation of a passing wave shows that 45 equally spaced peaks pass the observation point every second. The wave is known to travel at 135 meters/second. What therefore is the distance between the peaks?
If 45 peaks pass in a second, then the section of the wave that passes in a second must contain 45 peaks.
Since the wave travels at 135 meters/second, the section of the wave that passes in a second must be 135 meters long.
Therefore there are 45 peaks in 135 meters.
The distance between peaks must therefore be
We call this distance between peaks the wavelength1 of the wave.
If f peaks per second pass at velocity v, then in time interval `dt, the number of peaks will be f `dt and the distance moved will be v `dt.
If there are f `dt peaks spread over distance v `dt, then the distance between peaks is v `dt / f `dt = v / f.
The figure below depicts the segment of the wave that will pass in time interval `dt. This segment has length v `dt. Since its frequency is f, which represents the number of peaks passing per unit of time, we also seen that the number of peaks is f `dt.
The distance between peaks is easily found by dividing the number of peaks into the distance over which they are spread. In this case the distance is
This distance is called the wavelength of the wave.
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