Q185 / 200 · WBJEE 2013 · Physics
A car moving at a velocity of $17 \mathrm{ms}^{-1}$ towards an approaching bus that blows a horn at a frequency of $640 \mathrm{Hz}$ on a straight track. The frequency of this horn appears to be $680 \mathrm{Hz}$ to the car driver. If the velocity of sound in air is $340 \mathrm{ms}^{-1}$, then the velocity of the approaching bus is
- A$2 \mathrm{ms}^{-1}$
- Correct answerB$4 \mathrm{ms}^{-1}$
- C$8 \mathrm{ms}^{-1}$
- D$10 \mathrm{ms}^{-1}$
Solution
Given, velocity of sound, $v=340 \mathrm{m} / \mathrm{s}$
Velocity of listner, $v_{L}=17 \mathrm{m} / \mathrm{s}$
Velocity of source $=v_{s}$
Frequency of hom emitted
$$
v=640 \mathrm{Hz}
$$
The apparent frequency
$$
\begin{aligned}
v^{\prime} &=v \frac{\left(v+v_{l}\right)}{v-v_{s}} \\
680 &=640\left(\frac{340+17}{340-v_{s}}\right)
\end{aligned}
$$
On solving we get $v_{s}=4 \mathrm{m} / \mathrm{s}$
The apparent frequency
$$
\begin{aligned}
v^{\prime} &=v \frac{\left(v+v_{l}\right)}{v-v_{s}} \\
680 &=640\left(\frac{340+17}{340-v_{s}}\right)
\end{aligned}
$$
On solving we get $v_{s}=4 \mathrm{m} / \mathrm{s}$Hence, the correct answer is option: 'B'.