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Set 56 Problem number 6


Problem

What is the velocity of propagation of a wave whose wavelength is 6 meters and frequency 36 Hz?

Solution

Our picture of a 1-second section of the wave will show 36 peaks (recall that Hz stands for Hertz, and means the number of cycles or peaks per second), with 6 meters between peaks.

This section will therefore be 36 * 6 meters = 216 meters long, and the wave will travel at 216 meters/second.

A 1-second section of the wave is 216 meters long, and has peaks so the wave must be moving at 216 m/s.

Generalized Solution

At velocity v, in time interval `dt the wave will move distance v `dt. If its frequency is f then in this time it will pass through f `dt complete cycles.

So f `dt cycles correspond to distance v `dt.

Each cycle must therefore occupy distance v `dt / f `dt = v / f.

This is the wavelength `lambda.

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