Physics - Sound Wave Question with Solution | TestHub

Given:
Speed of sound, $v=330\text{m/s}$
Speed of trains, $v_s=30\text{m/s}$
Actual frequency, $f_0=300\text{Hz}$

Apparent frequency of train A (moving towards the observer):
$f_A=f_0\left(\frac{v}{v-v_s}\right)$
$f_A=300\left(\frac{330}{330-30}\right)=300\left(\frac{330}{300}\right)=330\text{Hz}$

Apparent frequency of train B (moving away from the observer):
$f_B=f_0\left(\frac{v}{v+v_s}\right)$
$f_B=300\left(\frac{330}{330+30}\right)=300\left(\frac{330}{360}\right)=275\text{Hz}$

Difference in frequencies heard by the person:
$\Delta f=f_A-f_B=330-275=55\text{Hz}$

Answer: $55\text{Hz}$