Question

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

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

Answer 1

Answer: (B)

$4m{s}^{-1}$

Given velocity of sound $v=340m/s$
Velocity of listner $v_L=17m/s$
Velocity of source $=v_S$
Frequency of horn emitted
$\nu =640Hz$
The apparent frequency
${\nu }^{\prime }=\nu \frac{(v+v_L)}{v-v_S}$
$680=640\left(\frac{340+17}{340-v_S}\right)$
On solving we get $v_S=4m/s$