Question

S is a stationary source of sound emitting waves of frequency $440\text{Hz}$. These waves are reflected by a stationary wall and heard by observer O moving away with $v=10\text{m/s}$. Find beat frequency (in Hz) heard by observer in the position shown (due to superposition between reflected and direct waves) $(V_{\text{sound}}=330\text{m/s})$

Answer 1

$f_{\text{direct}}=440\text{Hz}$
$f_{\text{indirect}}=440\left[\frac{330-10\text{cos}{53}^{\circ }}{330}\right]$

$=440\left[1\right]-\frac{40}{3}\left(\frac{3}{5}\right)$
$=440-8\Rightarrow 432\text{Hz}$
$\Delta f=440-432=8\text{Hz}$