Question

A car is moving towards a fixed wall. It blows a horn of frequency $440\text{Hz}$. The frequency of reflected sound observed by the driver is $480\text{Hz}$. Then, find the speed of the car in $\text{km/hr}$. $($Speed of sound in air is $350\text{m/s}$$)$

• A. $64.78\text{km/hr}$
• B. $26.78\text{km/hr}$
• C. $54.78\text{km/hr}$
• D. $47.78\text{km/hr}$

Answer 1

The correct option is C $54.78\text{km/hr}$

Before reflection of sound, the horn of the car will act as source and the fixed wall as observer.

From Doppler's effect formula, frequency received at the wall
$f_1=\left(\frac{v+v_o}{v-v_s}\right)\times f_0=\left(\frac{v}{v-u}\right)\times f_0$ ...$\left(1\right)$
where $f_0=440\text{Hz}$

After reflection of sound, fixed wall will act as source emitting frequency $f_1$ and the driver of the car as observer.

So, frequency observed by the driver
$f_2=\left(\frac{v+v_o}{v-v_s}\right)\times f_1=\left(\frac{v+u}{v}\right)\times f_1$ ...(2)

From $\left(1\right)$ and $\left(2\right)$,
$f_2=\left(\frac{v+u}{v}\right)\times \left(\frac{v}{v-u}\right)\times f_0$
$\Rightarrow f_2=\left(\frac{v+u}{v-u}\right)\times f_0$
$\Rightarrow 480=\left(\frac{350+u}{350-u}\right)\times 440$
$\Rightarrow \frac{12}{11}=\frac{350+u}{350-u}$
$\Rightarrow 12\times 350-12\times u=11\times 350+11\times u$
$\Rightarrow 23u=350$
$\Rightarrow u=\frac{350}{23}\text{m/s}=\frac{350}{23}\times \frac{18}{5}=54.78\text{km/hr}$

Why this question? It tests your recalling power for the formula of Doppler's effect to apply in different cases.