Question

A sound wave of frequency $f$ 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 study following statements
(i) The frequency of the reflected wave is $\frac{f(c+v)}{c-v}$
(ii) The wavelength of the reflected wave is $\frac{c(c-v)}{f(c+v)}$
(iii) The number of waves striking the surface per second is $\frac{f(c+v)}{c}$
(iv) The number of beats heard by a stationary listener to the left of the reflecting surface is $\frac{f v}{c-v}$ Correct statements are

• A. (i),(ii) and (iii)
• B. (i),(ii) and (iv)
• C. (ii),(iii) and (iv)
• D. (i),(iii) and (iv)

Answer 1

Answer: (A)

Number of waves striking the surface per second (or the frequency of the waves reaching surface of the moving target )
$ n^{\prime}=\frac{(c+v)}{\lambda}=\frac{f(c+v)}{c}$
Now these waves are reflected by the moving target
(Which now act as a source). Therefore apparent frequency of reflected second
$n^{\prime \prime}=\left(\frac{c}{c-v}\right) n^{\prime}=f\left(\frac{c+v}{c-v}\right)$
The wavelength of reflected wave $=\frac{c}{n^{\prime \prime}}$
$=\frac{c(c-v)}{f(c+v)}$ The number of beats heard by stationary listener
$=n^{\prime \prime}-f=f\left(\frac{c+v}{c-v}\right)-f=\frac{2 f v}{(c-v)}$
Hence option (a) is correct.