A point source of sound $S$ of natural frequency $256\text{ Hz}$ and a receiver $R$ are moving along same…
A point source of sound $S$ of natural frequency $256\text{ Hz}$ and a receiver $R$ are moving along same line with speed $u = 20\text{ ms}^{-1}$ towards a reflecting surface which is approaching them with speed $u$ as shown in figure.
If speed of sound in air is $330\text{ ms}^{-1}$, then wavelength and frequency of reflected wave received by $R$ are respectively
$\frac{330}{289}\text{ m and } 289\text{ Hz}$
$\frac{340}{289}\text{ m and } 289\text{ Hz}$
$\frac{330}{272}\text{ m and } 289\text{ Hz}$
$\frac{340}{272}\text{ m and } 289\text{ Hz}$
Solution
Let the reflecting surface be at rest.
[Diagram shows source $S$, reflector $R$, and image source $S'$ moving with velocities $20\text{ ms}^{-1}$.]
$f' = 256 \left( \frac{330 + 20}{330 - 20} \right) \text{ Hz} = 289\text{ Hz}$
and $\lambda' = \frac{v'}{f'} = \frac{(330 + 10)}{289} = \frac{340}{289}\text{ m}$