A sound wave of frequency $\nu$ travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with a speed $v.$ The speed of sound in the medium is $c,$ then
IIT 1995, Diffcult
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(d) Number of waves striking the surface per second (or the frequency of the waves reaching surface of the moving target )
$n' = \frac{{(c + v)}}{\lambda }$$ = \frac{{\nu (c + v)}}{c}$
Now these waves are reflected by the moving target
(Which now act as a source). Therefore apparent frequency of reflected second $n'' = \left( {\frac{c}{{c - v}}} \right)n'$ $ = \nu \left( {\frac{{c + v}}{{c - v}}} \right)$
The wavelength of reflected wave $n = \left( {\frac{c}{{c - v}}} \right)n'$
The number of beats heard by stationary listener $ = n'' - \nu = \nu \left( {\frac{{c + v}}{{c - v}}} \right) - \nu = \frac{{2\nu v}}{{(c - v)}}$
Hence option $(a)\, (b)$ and $(c)$ are correct.
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