Question

A car moving at a velocity of $17m{s}^{-1}$ 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 velociy of sound in air is $340m{s}^{-1}$, then 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 : $f=680$ Hz $f_o=640$ Hz

Velocity of car (observer) $v_o=17m/s$

Velocity of sound $v_{sound}=340m/s$

Let the velocity of bus (source) be $v_s$.

Using Doppler effect in case a source moves towards an approaching observer.

Apparent frequency $\left(f\right)$ heard by the car driver (observer) $f=f_o[\frac{v_{sound}+v_o}{v_{source}-v_s}]$

$\therefore$ $680=640[\frac{340+17}{340-v_s}]$

OR $340-v_s=336$ $⟹$ $v_s=4$ $m/s$