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Q.

The difference between the apparent frequency of a source of sound as perceived by an observer during its  approach and recession  is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/sec, the velocity of the source is (It is given that velocity of source << velocity of sound)The difference between the apparent frequency of a source of sound as perceived by an observer during its  approach and recession  is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/sec, the velocity of the source is (It is given that velocity of source << velocity of sound)

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a

6 m/sec

b

3 m/sec

c

1.5 m/sec

d

12 m/sec

answer is B.

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Detailed Solution

When the source approaches the observer  Apparent frequency  n'=vv−vs.n=n11−vsv=  n1−vsv−1=n1+vsv(Neglecting higher powers because vS << v)When the source recedes the observed apparent frequency  n''=n1−vsvGiven n'−n''=2100n,  v=300 m/sec∴2100n=n1+vsv−n1−vsv=n2vsv⇒2100=2vsv⇒vs=v100=300100=3 m/sec
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