First slide

Doppler

Question

A source and an observer are situated on two perpendicular tracks as shown in the figure. The observer is at rest and source is moving with a speed 50 m/s towards the observer. The source emits sound waves of frequency 90 Hz which travel in the medium with velocity 200 m/s. The frequency of sound heard by observer when the source crosses the origin O is

Difficult

A

84 Hz
B

88 Hz
C

92 Hz
D

96 Hz

Solution

When source is at origin, the observer receives the sound emitted by the source, when it was at P.
$S u c h t h a t \cos θ = \frac{50 t}{200 t} = \frac{1}{4}$
$\begin{array}{l} υ = \frac{v_{0} (υ)}{v - v_{s} \cos θ} = \frac{90 x 200}{200 - \frac{50}{4}} \\ υ = 96 H Z \end{array}$

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