JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Waves & Sound

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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

)

(A)16, 14
(B)12, 16
(C)8, 18
(D)12, 18✓ Correct

Answer: (D)

Solution

Treat the source as fixed and the observer as moving, so

f^{'} = f \frac{v \pm v _{o}}{v}

. Hearing

530

Hz means approaching:

530 = 500 \frac{300 + v _{o}}{300}

gives

v_{o} = 18

m/s. Hearing

480

Hz means receding:

480 = 500 \frac{300 - v _{o}}{300}

gives

v_{o} = 12

m/s. The two speeds are

12

m/s and

18

m/s.

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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