Question

A car is moving with a speed of $72km{h}^{-1}$ towards a roadside source that emits sound at a frequency of $850Hz$. The car driver listens to the sound while approaching the source and again while moving away from the source after crossing it. If the velocity of sound is $340{ms}^{-1}$, the difference of the two frequencies, the driver hears is:

• A. $50Hz$
• B. $85Hz$
• C. $100Hz$
• D. $150Hz$

Answer 1

The correct option is C $100Hz$

Given : Velocity of driver (observer) $v_o=72$ $km/h=20m/s$

Actual frequency of the source $\nu =850Hz$

Velocity of sound in air $v=340m/s$

Using Doppler effect when the observer moves towards the stationary source :

${\nu }^{\prime }=\nu [\frac{v+v_o}{v}]=850[\frac{340+20}{340}]$ $⟹{\nu }^{\prime }=900Hz$

Using Doppler effect when the observer moves away from the stationary source :

${\nu }^{\prime \prime }=\nu [\frac{v-v_o}{v}]=850[\frac{340-20}{340}]$ $⟹{\nu }^{\prime }=800Hz$

$\therefore$ Difference of the two frequency heard $\Delta \nu ={\nu }^{\prime }-{\nu }^{\prime \prime }=900-800=100Hz$