Question

The apparent frequency of a note is $200Hz$. When a listener is moving with a velocity of $40m{s}^{-1}$ towards a stationary source. When he moves away from the same source with the same speed, the apparent frequency of the same note is $160Hz$. The velocity of sound in air in $m/s$ is

• A. 340
• B. 330
• C. 360
• D. 320

Answer 1

Answer: (C)

When listener is moving towards the source then apparent frequency
$n^{\prime }=\frac{v+v_o}{v}\times n$
$\Rightarrow 200=\frac{v+40}{v}\times n\dots (i)$
where $v=$ velocity of sound in air
$n=$ actual frequency of sound source
Similarly, when listener is moving away,
then $160=\frac{v-40}{v}\times n\dots (ii)$
From Eqs. (i) and (ii), we have
$\frac{200}{160}=\frac{v+40}{v-40}$
$5v-200=4v+160$
$\therefore V=360m/s$