Question

A stationary source emits sound waves of frequency $500Hz$. Two observers moving along a line passing through the source detect sound to be of frequencies $480Hz$ and $530Hz$. Their respective speeds are, in $m{s}^{-1}$,( Given speed of sound $=300m/s$)

• A. $12,16$
• B. $16,14$
• C. $8,3318$
• D. $12,18$

Answer 1

The correct option is D $12,18$

Formula used: $f=\frac{v+v_0}{v-v_s}{f}_0$

Given
Frequency of source, $f=500Hz$

Apparent frequency received by observer $\text{'}1\text{'}$,

$f=480=\frac{300-v_1}{300}\times 500$

$\frac{1440}{5}=300-v_1$

$v_1=\frac{60}{5}=12m/s$

Apparent frequency received by observer $\text{'}2\text{'}$,

$530=\frac{300+v_2}{300}\times 500$

$1590=1500+5v_2$

$5v_2=90$

$v_2=18m/s$