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Sound Wave:Displacement Equation

A whistle giv...

Question

A whistle giving out 450Hz approaches a stationary observer at a speed of 32m/s. The frequency heard by the observer in Hz is nearly (velocity of sound in air = 330m/s)

A

500

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B

517

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C

429

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D

409

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Solution

The correct option is A 500
Given :
$V_{s} = 32 m / s$
$V_{0} = 0 m / s$
$δ = 450 H z$
$V = 330 m / s$
By doppler effect formula:
$δ^{1} = δ (\frac{V - V_{0}}{V - V_{s}})$
$= 450 (\frac{330 - 0}{330 - 32})$
$= \frac{450 \times 330}{298}$
$= 500 H z$

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