wave_mechanics critical_thinking Question 11
Question: 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)
[CPMT 1982; RPET 1998]
Options:
A) 6 m/sec
B) 3 m/sec
C) 1.5 m/sec
D) 12 m/sec
Show Answer
Answer:
Correct Answer: B
Solution:
When the source approaches the observer Apparent frequency $ n’=\frac{v}{v-v _{s}}.n=n[ \frac{1}{1-\frac{v _{s}}{v}} ] $ =$ n{{[ 1-\frac{v _{s}}{v} ]}^{-1}}=n[ 1+\frac{v _{s}}{v} ] $ (Neglecting higher powers because vS « v) When the source recedes the observed apparent frequency $ {n}’’=n[ 1-\frac{v _{s}}{v} ] $ Given $ n’-n’’=\frac{2}{100}n,v=300 $
$ m/\sec $
$ \therefore $
$ \frac{2}{100}n=n[ 1+\frac{v _{s}}{v} ]-n[ 1-\frac{v _{s}}{v} ]=n[ 2\frac{v _{s}}{v} ] $
$ \Rightarrow $ $ \frac{2}{100}=2\frac{v _{s}}{v}\Rightarrow v _{s}=\frac{v}{100}=\frac{300}{100}=3 $
$ m/\sec $ .
BETA
