Question

A boat at anchor is rocked by waves whose crests are 100 m apart and the velocity is $25{m}/{\sec }\;$. The boat bounces up once in every:
A. 2500 s
B. 75 s
C. 4 s
D. 0.25 s

Answer 1

The formula that relates the wavelength, frequency and the velocity should be used to solve this problem. As the wavelength is given in terms of crests of a wave and the value of the velocity of the wave is given, using these, we will find the value of the frequency. The reciprocal the frequency will be the time period, that is, the number of times the boat bounces.
Formula used:
$f=\dfrac{v}{\lambda }$

Complete answer:
The formula that relates the wavelength, frequency and the velocity is given as follows.
$f=\dfrac{v}{\lambda }$
Where f is the frequency of the wave, v is the velocity of the wave and$\lambda$ is the wavelength of the wave.
From the data, we have the data as follows.
A boat at anchor is rocked by waves whose crests are 100 m apart. So, $\lambda =100m$
The velocity of the wave is $25{m}/{\sec }\;$. So, $v=25{m}/{\sec }\;$
Substitute these values in the above formula to find the value of the frequency of the wave. So, we get,

& f=\dfrac{25}{100} \\\ & f=\dfrac{1}{4} \\\ \end{aligned}$$ We know that the time period is the reciprocal of the frequency. So, the time period of the wave is given as follows. $$\begin{aligned} & T=\dfrac{1}{f} \\\ & T=4\,s \\\ \end{aligned}$$ $$\therefore $$ The boat bounces up once in every 4 s. As the boat bounces up once in every 4 s. **Thus, the option (C) is correct.** **Note:** The question is a bit confusing while considering the value of the wavelength. They haven’t directly mentioned the value of the wavelength, in terms of crests the value is given. Even, directly the value of the frequency can be asked instead of the time period. The units of the parameters should be taken care of.