Question

The driver of a bus, approaching a big wall, notices that the frequency of his bus’s horn changes from $420\text{Hz}\text{to}490\text{Hz}$ when he hears it after it gets reflected from the wall. Find the speed of the bus, if the speed of the sound is $330{\text{ms}}^{–1}$

• A. $91{\text{km h}}^{-1}$
• B. $81{\text{km h}}^{-1}$
• C. $61{\text{km h}}^{-1}$
• D. $71{\text{km h}}^{-1}$

Answer 1

The correct option is A $91{\text{km h}}^{-1}$

From the Doppler's effect of sound, frequency appeared/heard at the wall is,

$f_w=\frac{330}{330-v}.f.....\left(i\right)$

Here,
$v\to$ speed of bus,
$f\to$ actual frequency of the source,

The frequency $\left(f^{\prime }\right)$ heard by the driver of the bus, after reflection from the wall is,

$f^{\prime }=\frac{330+v}{330}.f_w=\frac{330+v}{330-v}.f$

$\Rightarrow 490=\frac{330+v}{330-v}\times 420$

$\Rightarrow v=\frac{330\times 7}{91}=25.38\text{m/s}$

$=25.38\times \frac{18}{5}\approx 91\text{km/hr}$

Hence, $\left(A\right)$ is the correct answer.