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Q.

The frequency of the sound of a car horn as perceived by an observer towards whom the car is moving differs from the frequency of the horn by 2.50/6. Assuming that the velocity of sound in air is 320 m/sec, the velocity of car is

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a

8 m/s

b

800 m/s

c

7.5 m/s

d

6 m/s

answer is A.

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Detailed Solution

$n^{'} = (\frac{V}{V - V_{s}}) n given that n = (\frac{102 \cdot 5}{100}) n \frac{102 \cdot 5}{100} n = (\frac{320}{320 - v_{s}}) n or 320 \times 100 = 320 \times 102 \cdot 5 - 102 \cdot 5 v_{s} or 102 \cdot 5 v_{s} = 320 [102 \cdot 5 - 100] = 320 \times 2 \cdot 5 v_{s} = \frac{320 \times 2 \cdot 5}{102 \cdot 5} \approx 7 .8 m / s \approx 8 m / s$

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