A boat at anchor is rocked by waves whose consecutive crests are 100 m apart. The wave velocity of the moving crests is 20 m/s. What is the frequency of rocking of the boat?

0.1 H z

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0.2 H z

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1 H z

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2 H z

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Solution

The correct option is C $0.2 H z$
The relationship between the frequency, wavelength and speed of sound or velocity is given as follows.
Frequency, $ν = \frac{w a v e v e l o c i t y, v}{w a v e l e n g t h, λ}$
The distance between two consecutive crests is equal to the wavelength of the wave, therefore, $λ = 100 m$
So, $ν = \frac{v}{λ} = \frac{20 m / s}{100 m} = 0.2 H z$
Hence, the frequency of the wave is 0.2 Hz.

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