Question

A siren emitting sound of frequency $800 \,Hz$ is going away from a static listener with a speed of $30 \,m / s$. Frequency of sound to be heard by the listener is (velocity of sound = $330 \,m / s )$

• A. $286.5\, Hz$
• B. $481.2 \,Hz$
• C. $733.3\,Hz$
• D. $644.8 \,Hz$

Answer 1

Answer: (C)

The apparent change in the frequency of the source due to relative motion between source and observer is known as Doppler's effect. The perceived frequency $\left(n^{\prime}\right)$ when listener is static and source is moving away is given by
$n^{\prime}=n\left(\frac{v}{v+v_s}\right)$
where $n$ is frequency of source, $v$ is velocity of sound and $v_s$ is velocity of source.
Putting $v=330\, m / s , v_s=30\, m / s , n=800\, Hz$.
$n^{\prime} =800 \times\left(\frac{330}{330+30}\right) $
$n^{\prime} =733.3 \,Hz$
In the limit when speed of source and observer are much lesser than that of sound $v_1$ the change in frequency becomes independent of the fact whether the source is moved or the detector.