Question

A car moving at a velocity of 17 $ms^{-1}$ towards an approaching bus that blows a horn at a frequency of $640\ Hz$ on a straight track. The frequency of this horn appears to be $680\, Hz$ to the car driver. If the velocity of sound in air is $340\,m\,s^{-1}$, then velocity of the approaching bus is

• A. 2 $ms^{-1}$
• B. 4 $ms^{-1}$
• C. 8 $ms^{-1}$
• D. 10 $ms^{-1}$

Answer 1

Answer: (B)

Given, velocity of sound, $v=340 \,m / s$
Velocity of listner, $v_{L}=17\, m / s$
Velocity of source
$=v_{S}$ Frequency of horn emitted
$v=640 \,Hz$

The apparent frequency
$v^{\prime}=v \frac{\left(v+v_{L}\right)}{v-v_{s}} $
$680=640\left(\frac{340+17}{340-v_{S}}\right)$
On solving we get $v_{S}=4 m / s$