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Question
A boy riding on his bike is going towards east at a speed of 4√2 m s−1. At a certain point he produces a sound pulse of frequency 1650 Hz that travels in air at a speed of 334 m s−1. A second boy stands on the ground 45° south of east from his. Find the frequency of the pulse as received by the second boy.
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Solution
Given:
Frequency of pulse produced by the bike \[f_0\]= 1650 Hz
Velocity of bike \[v_b\] =4\[\sqrt{2}\]ms−1
Velocity of sound in air v = 334 ms−1
Frequency of pulse received by the second boy \[f\]= ?
Velocity of an observer \[v_0\]= 0
Velocity of source will be : \[v_s = v_b \cos\theta\]
=\[4\sqrt{2} \times \cos {45}^\circ\]
=\[4\sqrt{2} \times \frac{1}{\sqrt{2}} = 4 {\text { ms }}^{- 1}\]
Frequency of pulse received by the second boy is given by:
\[f = \left( \frac{v}{v - v_s} \right) f_0 \]
\[ = \left( \frac{334}{334 - 4} \right) \times 1650\]
\[ = 1670 \text { Hz }\]
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