Physics - Sound Wave Question with Solution | TestHub

Velocity of the train (source), $v_s=72\text{ km/hr}=72\times \frac{5}{18}\text{ m/s}=20\text{ m/s}$

Velocity of sound, $v=320\text{ m/s}$

Actual frequency, $f_0=510\text{ Hz}$

Observer is at rest, so $v_o=0$

When the train approaches the station, the apparent frequency $f_1$ is given by:

$f_1=f_0\left(\frac{v}{v-v_s}\right)$

$f_1=510\left(\frac{320}{320-20}\right)=510\left(\frac{320}{300}\right)=544\text{ Hz}$

When the train recedes from the station, the apparent frequency $f_2$ is given by:

$f_2=f_0\left(\frac{v}{v+v_s}\right)$

$f_2=510\left(\frac{320}{320+20}\right)=510\left(\frac{320}{340}\right)=480\text{ Hz}$

Answer: 544,480