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 $Hz$ .

1210

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Solution

Given :-
$V_{s} = V_{x} = 36 km/h = 36 \times \frac{5}{18} = 10 m/s$
$V_{o} = V_{y} = 72 km/h = 72 \times \frac{5}{18} = 20 m/s$
$V = 340 m/s$
$f = 1320 Hz$
Using Doppler's law :
$f = f_{o} (\frac{V + V_{o}}{V - V_{s}})$
$1320 = f_{o} (\frac{340 + 20}{340 - 10})$
$\Rightarrow f_{o} = 1210 Hz$

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