Question

The frequency of the sound of a car horn, as recorded by an observer towards whom the car is moving differs from the frequency of the horn by 10%. Assuming the velocity of sound in air to be $330m{s}^{-1}$, the velocity of the car is

• A. $36.7m{s}^{-1}$
• B. $40m{s}^{-1}$
• C. $30m{s}^{-1}$
• D. $33m{s}^{-1}$

Answer 1

Answer: (C)

$30m{s}^{-1}$

Given : $\frac{{\delta }^{{}^{\prime }}}{{\delta }^0}=\frac{110}{100}$

$v=330m/s$

$v_0=0m/s$

By doppler effect formula

${\delta }^{{}^{\prime }}=\delta \left(\frac{v-v_0}{v-v_3}\right)$

$\frac{{\delta }^{{}^{\prime }}}{\delta }=\left(\frac{v-v_0}{v-v_3}\right)$

$\frac{110}{100}=\left(\frac{330}{330-v_s}\right)$

$(330-v_s)110=330\times 100$

$330-v_s=300$

$330-300=v_s$

$\Rightarrow v_s=30m/s$