Question

A bus driving at 39.6 km/h is approaching a person who is standing at the bus stop, while honking repeatedly at an interval of 30 seconds. If the speed of the sound is $330m{s}^{-1}$ , at what interval will the person hear the horn?

• A. 31 seconds
• B. 29 seconds
• C. 30 seconds
• D. The interval will depend on the distance of the bus from the passenger.

Answer 1

The correct option is B 29 seconds

Solution

Applying Doppler Effect in sound:

$f_0=f\left(\frac{v+v_0}{v-v_s}\right)$

$v\to$ speed of sound = 330 m/s

$v_0\to$ speed of observer = 0 m/s

$v_s\to$ speed of fource = 39.6 km/hr

$=39.6\times \frac{5}{18}m/s=11m/s$

$f\to$ sound frequency = $\frac{1}{Timeperiod}=\frac{1}{30}Hz$

$f_0\to$ heard sound frequency = $\frac{1}{T^{\prime }}$

So, $\frac{1}{T^{\prime }}=\frac{1}{30}\left(\frac{330+0}{330-11}\right)$

$T^{\prime }=\left(30\right)\left[\frac{330-11}{330}\right]=30\left[\frac{1-1}{30}\right]$

$T^{\prime }=29s$

At interval of 29 s the sound will be

heard.

Option - B is correct.