JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Waves & Sound

Two cars X and Y are approaching each other with velocities

36 km / h

and

72 km / h

respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is

340 m / s

, the actual frequency of the whistle sound produced is ______ Hz.

Answer: 1210

Solution

Converting speeds,

v_{X} = 36 km/h = 10 m/s

and

v_{Y} = 72 km/h = 20 m/s

, both approaching. With source X and observer Y,

f^{'} = f_{0} \frac{v + v _{Y}}{v - v _{X}} = f_{0} \frac{340 + 20}{340 - 10} = f_{0} \frac{12}{11} .

Setting

f^{'} = 1320

Hz gives

f_{0} = 1320 \times \frac{11}{12} = 1210

Hz.

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Integer answer

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