Question

A car travelling towards a hill at 10 m/s sounds its horn which has a frequency 500 Hz. This is heard in a second ear travelling behind the first car in the same direction with speed 20 m/s. The sound can also be heard in the second car will be :

(speed of sound in air = 340 m/s)

• A. 31 Hz
• B. 24 Hz
• C. 21 Hz
• D. 34 Hz

Answer 1

The correct option is A 31 Hz

Velocity of car A $v_A=10m/s$ and velocity of car B $v_B=20m/s$

Original frequency of car A $f=500Hz$

Let $f_d$ and $f^{\prime \prime }$ be the apparent frequencies (heard by person in car B) coming directly and after reflection from the hill respectively.

Doppler effect when observer $\left(B\right)$ moves towards the moving source $\left(A\right)$:

$f_d=f[\frac{v_{sound}+v_{observer}}{v_{sound}+v_{source}}]$ $=500[\frac{340+20}{340+10}]=514.28Hz$

Doppler effect when source $\left(A\right)$ moves towards the stationary observer $\left(Hill\right)$:

$f^{\prime }=f[\frac{v_{sound}}{v_{sound}-v_{source}}]$ $=500[\frac{340}{340-10}]=515.15Hz$

Doppler effect when observer $\left(B\right)$ moves towards the stationary source $\left(Hill\right)$:

$f^{\prime \prime }=f^{\prime }[\frac{v_{sound}+v_{observer}}{v_{sound}}]$ $=515.15[\frac{340+20}{340}]=545.45Hz$

Now beats heard in the car B $b=f^{\prime \prime }-f_d=545.45-514.28\approx 31Hz$