Question

In the figure shown, a source of sound of frequency $510$ Hz moves with constant velocity $v_s=20\text{m/s}$ in the direction shown. The wind is blowing at a constant velocity $v_w=20\text{m/s}$ towards an observer who is at rest at point B. Find the frequency (in Hz) detected by the observer corresponding to the sound emitted by the source at initial position A. (speed of sound relative to air = $330$ m/s)

Answer 1

Let, the sound wave frequency be $v=510$ Hz
The speed of sound relative to air is $u=330m{s}^{-1}$
Now, the apparent frequency of sound detected by observer is
$v^{\prime }=v\left(\frac{u+v_w}{u+v_w-v_s\text{cos}{60}^{\circ }}\right)$ (from figure)
$v^{\prime }=510\left(\frac{330+20}{330+20-20\text{cos}{60}^{\circ }}\right)$ (given)
$v^{\prime }=510\left(\frac{350}{350-10}\right)$
$v^{\prime }=510\left(\frac{350}{340}\right)$
v' = 525 Hz