Question

A sound wave of frequency f travels horizontally to the right. It is reflected from a large vertical plane surface moving to left with a speed $v$. If the speed of sound in medium is $c$, then

• A. The frequency of reflected wave is $\frac{f(c+v)}{(c-v).}$
• B. The wavelength of reflected wave is $\frac{c(c-v)}{f(c+v)}$.
• C. The number of wave striking the surface per second is $\frac{f(c+v)}{c}$.
• D. The number of beats heard by a stationary listener to the left to the reflecting surface is $\frac{vf}{(c-v)}$.

Answer 1

Answer: (A), (B), (C)

The correct options are
A The frequency of reflected wave is $\frac{f(c+v)}{(c-v).}$
B The wavelength of reflected wave is $\frac{c(c-v)}{f(c+v)}$.
C The number of wave striking the surface per second is $\frac{f(c+v)}{c}$.

Number of waves encountered by the moving plane per unit time$=$ $\frac{\mathrm{distance}\mathrm{travelled}}{\mathrm{wavelength}}$
$=\frac{c+v}{\lambda }=\frac{c}{\lambda }(1+\frac{v}{c})=f(1+\frac{v}{c})$
$f^{\prime }$ is the frequency of the incident wave and $f^{\prime \prime }$ is the frequency of the reflected wave that a stationary observer meets.

$f\text{'}\text{'}=\frac{f\text{'}}{\left(}=\frac{f\left(1+\frac{v}{c}\right)}{\left(}=\frac{f(c+v)}{(c-v)}$$\lambda \text{'}\text{'}=\frac{c}{f\text{'}\text{'}}=\frac{c}{f}\left(\frac{c-v}{c+v}\right)$
Beat frequency$=f^{\prime \prime }-f$
$=\frac{f(c+v)}{(c-v)}-f=\frac{2vf}{(c-v)}$