Question

A car travelling at $10m{s}^{-1}$ sounds a horn, which has a frequency of $500Hz$ and this is heard in another car, which is travelling behind the first car, in the same direction, with the velocity of $20m{s}^{-1}$. The sound can also be heard in the second car by reflection from a bridge ahead. What frequencies will the driver of the second car can hear (approximately) ? (speed of sound in air = $340m{s}^{-1}$)

• A. $514Hz,528Hz$
• B. $514Hz,545Hz$
• C. $509Hz,545Hz$
• D. $528Hz,564Hz$

Answer 1

The correct option is B $514Hz,545Hz$

In the first case, when sound is directly coming to the second car, it is the case of observer moving at a speed $u=10m/s$.
Apparent frequency $\nu =\frac{v+u}{v}{\nu }_0=514.7Hz$, where $v=340\text{m/s}$ and ${\nu }_0=500Hz$
Second case, when the reflected sound comes from the bridge,
Apparent frequency at the bridge
${\nu }_{wall}=\frac{v}{v-u_1}{\nu }_0$
Here $u_1=10m/s$ (velocity of the first car)
Thus ${\nu }_{wall}=\frac{340}{340-10}500=515.2$
Now the apparent frequency of the reflected sound at the second car is
${\nu }_r=\frac{v+u_2}{v}{\nu }_{wall}$, where $u_2=20\text{m/s}$
Hence ${\nu }_r=545.5\text{Hz}$