Q180 / 180 · COMEDK 2019 · Physics
The difference between the apparent frequency of a source of sound as perceived by the observer during its approach and recession is $2 \%$ of the frequency of the source. If the speed of sound in air is $300 \mathrm{~ms}^{-1}$, then the velocity of the source is
- A$6 \mathrm{~ms}^{-1}$
- Correct answerB$3 \mathrm{~ms}^{-1}$
- C$1.5 \mathrm{~ms}^{-1}$
- D$12 \mathrm{~ms}^{-1}$
Solution
Given, speed of sound in air, $c=300 \mathrm{~ms}^{-1}$
Difference between apparent frequency during approach and apparent frequency duifing recession $=2 \%$
Thus, frequency during approach - frequency during recession $=\frac{2}{100} \times f_{0}$
$$
\Rightarrow \quad f_{0}\left(\frac{c+v}{c}\right)-f_{0}\left(\frac{c-v}{c}\right)=\frac{2}{100} f_{0}
$$
where, $c$ is speed of sound in air and $v$ is the velocity of source.
$$
\begin{array}{llrl}
\Rightarrow & & \frac{2 v}{300} & =\frac{2}{100} \\
\Rightarrow & v & =3 \mathrm{~ms}^{-1}
\end{array}
$$
Hence, the correct answer is option: 'B'.