Physics - Sound Wave Question with Solution | TestHub

Given:
Speed of the trains (source), $v_s=30\text{ m/s}$
Actual frequency of sound, $n=300\text{ Hz}$
Speed of sound in air, $v=330\text{ m/s}$

When the first train approaches the stationary observer, the apparent frequency heard is:
$n_1=n\left(\frac{v}{v-v_s}\right)$
$n_1=300\left(\frac{330}{330-30}\right)=300\left(\frac{330}{300}\right)=330\text{ Hz}$

When the second train moves away from the stationary observer, the apparent frequency heard is:
$n_2=n\left(\frac{v}{v+v_s}\right)$
$n_2=300\left(\frac{330}{330+30}\right)=300\left(\frac{330}{360}\right)=300\times \frac{11}{12}=275\text{ Hz}$

The difference in frequencies heard by the person is:
$\Delta n=n_1-n_2=330-275=55\text{ Hz}$

Answer: 55 Hz