Question

The distance between $2^{nd}$ crest and $6^{th}$ trough of a wave shown below is $24cm$. If the wave velocity of the moving crests is $20m{s}^{-1}$, then frequency of rocking of the boat is

• A. $24Hz$
• B. $20Hz$
• C. $375Hz$
• D. $240Hz$

Answer 1

The correct option is C $375Hz$

The distance between two consecutive crests or troughs is known as wavelength$\left(\lambda \right)$

Hence the distance between the $2^{nd}$ crest and the $6^{th}$ crest will be $4\lambda$

The distance between any crest and its successive trough is $\frac{\lambda }{2}$

Hence the distance between the $2^{nd}$ crest and the $6^{th}$ trough will be $4.5\lambda$

The frequency of rocking of the boat is same as the frequency(f) of the wave

We know that velocity $\left(v\right)=f\lambda$

$\therefore f=\frac{v}{\lambda }$ $\because 4.5\lambda =0.24,$ $\lambda =\frac{0.24}{4.5}$

$\therefore f=\frac{20}{\left(\frac{0.24}{4.5}\right)}=\frac{20\times 4.5}{0.24}=\frac{90\times 100}{6\times 4}=15\times 25=375Hz$