A source of sound is approaching an observer with speed of $30\ \mathrm{ms}^{-1}$ and the observer is…
A source of sound is approaching an observer with speed of $30\ \mathrm{ms}^{-1}$ and the observer is approaching the source with a speed of $50\ \mathrm{ms}^{-1}$. Find the fractional change in the frequency of sound (speed of sound in air = $330\ \mathrm{ms}^{-1}$).
Solution
Sol. Given, $v_s = 30\ \mathrm{ms}^{-1} \Rightarrow v_0 = 50\ \mathrm{ms}^{-1}$
Apparent frequency, $f' = f \left[\frac{v + v_0}{v - v_s}\right]$
$\Rightarrow f' = f \left[\frac{330 + 50}{330 - 30}\right]$
$\Rightarrow f' = f \left[\frac{380}{300}\right]$
$\Rightarrow f' = f \left[\frac{38}{30}\right]$
\nTherefore fractional change in frequency,
$\left(\frac{f' - f}{f}\right) = \frac{38 - 30}{30} = \frac{8}{30} = \frac{4}{15}$
Answer: $\frac{4}{15}$