Question

A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound then the velocity of the car is

• A. $\frac{v}{\sqrt{2}}$
• B. $\frac{v}{2}$
• C. $\frac{v}{3}$
• D. $\frac{v}{4}$

Answer 1

Answer: (C)

$\frac{v}{3}$

Let velocity of car $=v$

$n^{{}^{\prime }}=n\left[\begin{array}{c}\frac{v}{v-v_s}\end{array}\right]\dots \left(i\right)n^{\prime \prime }=n^{{}^{\prime }}\left[\begin{array}{c}\frac{v+v_s}{v}\end{array}\right]\dots \left(ii\right)$

From (i) & (ii) $n^{\prime \prime }=n\left[\begin{array}{c}\frac{v+v_s}{v-v_s}\end{array}\right]$

Now $\frac{n^{\prime \prime }}{n}=2\Rightarrow \left(\begin{array}{c}\frac{v+v_s}{v-v_s}\end{array}\right)=2$

$\Rightarrow v+v_s=2v-2v_s\Rightarrow 3v_s=v\Rightarrow v_s=\frac{v}{3}$