A source of sound $S$ is moving with a velocity of $50\text{ ms}^{-1}$ towards a stationary observer. The…
A source of sound $S$ is moving with a velocity of $50\text{ ms}^{-1}$ towards a stationary observer. The observer measures the frequency of the source as $1000\text{ Hz}$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (The velocity of the sound in the medium is $350\text{ ms}^{-1}$.)
750 Hz
857 Hz
1143 Hz
1333 Hz
Solution
When the source is coming to the stationary observer,
$n' = \left(\frac{v}{v - v_s}\right) n$
$\Rightarrow 1000 = \left(\frac{350}{350 - 50}\right) n$
or $n = \frac{1000 \times 300}{350}\text{ Hz}$
When the source is moving away from the stationary observer,
$n'' = \left(\frac{v}{v + v_s}\right) n$
$= \left(\frac{350}{350 + 50}\right) \left(\frac{1000 \times 300}{350}\right) = 750\text{ Hz}$