Question

A body is moving forward and backward. Change in frequency observed by the body of a source is $2 \%$. What is velocity of the body? (Speed of sound is $300\, ms ^{1}$ )

• A. $6\, ms^{-1}$
• B. $2\, ms^{-1}$
• C. $2.5\, ms^{-1}$
• D. $3\, ms^{-1}$

Answer 1

Answer: (D)

$3\, ms^{-1}$

Answer 2

Here, body is acting as an observer.
According to the given case, let $u$ be the velocity of the body
then, $v_{1}=v\left(\frac{v-u}{v}\right)$
and $v_{2}=v\left(\frac{v+ u}{v}\right)$
$\therefore \Delta v=v_{2}-v_{1}=v \frac{2 u}{v}$
So, $\frac{\Delta v}{v} \times 100=\frac{2 u}{v} \times 100$
or $2=\frac{2 u}{v} \times 100$
or $u=\frac{v}{100}=3\, ms ^{-1}$