What is the velocity of a wave whose wavelength is .157 meters and whose cycles have a period of .000026 second?
A single cycle, from peak to peak, is .157 meters long and passes in .000026 second. The wave therefore travels .157 meters in a time interval of .000026 second.
The wave must therefore be traveling at .157 meters / .000026 sec = 6038 meters/second.
A wave whose wavelength is `lambda, completing a period in time T, must move distance `lambda in time T. Its velocity must therefore be `lambda / T.
We note that the frequency of the wave is the reciprocal of T: frequency = f = 1 / T. Thus v = `lambda / T = f * `lambda, consistent with our knowledge that v = f `lambda.
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