A car sounding its horn at $480\text{ Hz}$ moves towards a high wall at a speed of $20\text{ ms}^{-1}$. The…
A car sounding its horn at $480\text{ Hz}$ moves towards a high wall at a speed of $20\text{ ms}^{-1}$. The frequency of the reflected sound heard by the man sitting in the car will be nearest to (speed of sound $= 330\text{ ms}^{-1}$)
$480\text{ Hz}$
$510\text{ Hz}$
$540\text{ Hz}$
$570\text{ Hz}$
Solution
The frequency of the reflected sound heard by man,
$f' = f \left( \frac{v + v_s}{v - v_s} \right) = 480 \left( \frac{330 + 20}{330 - 20} \right) = 541.9\text{ Hz} \approx 540\text{ Hz}$
[Diagram showing observer O, source S moving towards a wall at $20\text{ ms}^{-1}$, and image source S' moving towards the wall at $20\text{ ms}^{-1}$.]