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Q.

The driver of a motor van approaching a vertical wall notices that the frequency of his van’s horn changes from 440 Hz to 480 Hz when it gets reflected from the wall. Find the speed of the van. (in KMPH)
(the speed of sound =330 m/s)

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answer is 52.

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Detailed Solution

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$v^{''} = \frac{v + u}{v} v^{'} = \frac{v + u}{v} . \frac{v}{v - u} v = \frac{v + u}{v - u} v .$
Putting the values,
$840 = \frac{v + u}{v - u} = 440$ or $\frac{v + u}{v - u} = \frac{48}{44}$ or $\frac{u}{v} = \frac{4}{92}$
Or $u = \frac{4}{92} \times 330 m / s = 14.3 m / s \approx 52 k m / h .$

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