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 $340m{s}^{-1}$, the difference between the two frequencies, the driver hears is

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

Answer 1

The correct option is C

$100Hz$

Step 1. Given data

Velocity of the observer, ${\nu }_0=72km{h}^{-1}$

$=20m{s}^{-1}$

Actual frequency of the source, $f=850Hz$

Velocity of the sound in the air, $\nu =340m{s}^{-1}$

Step 2, Finding the difference between the two frequency, $∆f$

Using the doppler effect, when the observer moves toward the stationary source

$f\text{'}=f\left(\frac{v+v_0}{v}\right)$

$f\text{'}=850\times \frac{\left(340+20\right)}{340}$

$f\text{'}=900Hz$

Using the doppler effect, when the observer moves away from stationary source

$f\text{'}\text{'}=f\frac{\left(v-v_0\right)}{v}$

$f\text{'}\text{'}=850\times \left(\frac{340-20}{340}\right)$

$f\text{'}\text{'}=800Hz$

Difference between two frequency

$∆f=f\text{'}-f\text{'}\text{'}$

$∆f=900-800$

$∆f=100Hz$

Hence, the correct option is $\left(C\right)$.