Question

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

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

Answer 1

The correct option is C 375 Hz

Distance between $2^{nd}$ crest and $6^{th}$ through
$=4\lambda +\frac{\lambda }{2}=\frac{9\lambda }{2}$
$\frac{9\lambda }{2}=24cm$
$\lambda =\frac{24\times 2}{9}cm=\frac{48}{9}cm$
$V=20m{s}^{-1}$
$v=\frac{V}{\lambda }=\frac{20}{48}\times 9\times 100Hz$
$=375Hz$