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

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

JEE MainJEE Main 2019Waves

Solution:

$f =480 = \frac{300 -v_{1}}{300} \times500 $
$ \frac{1440}{5} = 300 - v_{1} $
$ v_{1} = \frac{60}{5} = 12m /s$
$ 530 = \frac{300+v_{2}}{300} \times500$
$ 1590 = 1500 + 5v_{2} $
$ 5v_{2} = 90 $
$ v_{2} = 18 \,m/s $