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

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 ... $m/sec$ (It is given that velocity of source $<<$ velocity of sound)

b (b) When the source approaches the observer Apparent frequency $n' = \frac{v}{{v - {v_s}}}.n = n\left[ {\frac{1}{{1 - \frac{{{v_s}}}{v}}}} \right]$ =$n{\left[ {1 - \frac{{{v_s}}}{v}} \right]^{ - 1}} = n\left[ {1 + \frac{{{v_s}}}{v}} \right]$ (Neglecting higher powers because $v_S << v$) When the source recedes the observed apparent frequency $n'' = n\left[ {1 - \frac{{{v_s}}}{v}} \right]$ Given $n' - n'' = \frac{2}{{100}}n,\,\,v = 300$$m/\sec $ $\therefore $ $\frac{2}{{100}}n = n\left[ {1 + \frac{{{v_s}}}{v}} \right] - n\left[ {1 - \frac{{{v_s}}}{v}} \right] = n\left[ {2\frac{{{v_s}}}{v}} \right]$ $ \Rightarrow $ $\frac{2}{{100}} = 2\frac{{{v_s}}}{v} \Rightarrow {v_s} = \frac{v}{{100}} = \frac{{300}}{{100}} = 3$$m/\sec $.

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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 ... $m/sec$ (It is given that velocity of source $<<$ velocity of sound)

A$6$
B$3$
C$1.5$
D$12$

Diffcult

STD 11 Science
NEET
STD 11 - 14. waves and sound
Physics

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