If a wave has the characteristic that 35 equally spaced peaks pass a given point every second, with the wave traveling at 70 meters/second, then what is wavelength of the wave?
If 35 peaks pass in a second, then the section of the wave that passes in a second must contain 35 peaks.
Since the wave travels at 70 meters/second, the section of the wave that passes in a second must be 70 meters long.
Therefore there are 35 peaks in 70 meters.
The distance between peaks must therefore be
We call this distance between peaks the wavelength 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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