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Set 56 Problem number 5


Problem

If a wave with wavelength 5 meters passes at 30 meters/second, how much time elapses between consecutive peaks?

Solution

A 1-second section of the wave is 30 meters long, and has peaks 5 meters apart. Each peak therefore spans 5/ 30 of the 1-second section. Therefore the time between peaks will be 5/ 30 seconds = .1666 seconds.

The time between peaks is also referred to as the time for a complete cycle, and is called the period of a cycle.

Generalized Solution

If the frequency of a wave in Hz is f and its wavelength is `lambda, then in time interval `dt we find that f `dt cycles of the wave, each of length `lambda, must pass. The length of this wave segment is therefore f `dt `lambda. The velocity is distance / time = f `dt `lambda / `dt = f `lambda.  We thus have

    v = f * `lambda (i.e., velocity = frequency * wavelength)

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