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Q.

The difference between the apparent frequencies of a source of sound as perceived by a stationary observer during its approach and recession is 2% of the actual frequency of the source. If the speed of sound is 300 m/s, the speed of source is

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a

1.5 m/s

b

3 m/s

c

6 m/s

d

12 m/s

answer is B.

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Detailed Solution

$\frac{f_{approach} - f_{recede}}{f} = \frac{∆ f}{f} = \frac{v}{v - v_{s}} - \frac{v}{v + v_{s}} ∴ \frac{∆ f}{f} = \frac{v (v + v_{s} - v + v_{s)}}{v^{2} - v_{s}^{2}} = \frac{2 {vv}_{s}}{v^{2} - v_{s}^{2}} But \frac{∆ f}{f} = \times 100 = 2 % \Rightarrow 0.02 = \frac{2 (300) v_{s}}{{(300)}^{2} - v_{s}^{2}} \Rightarrow 0.02 = \frac{2 (300) v_{s}}{{(300)}^{2}} = \frac{2}{300} v_{s} v_{s} = (0.01) 300 = 3 m / s$

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The difference between the apparent frequencies of a source of sound as perceived by a stationary observer during its approach and recession is 2% of the actual frequency of the source. If the speed of sound is 300 m/s, the speed of source is