Question

A source of sound is moving with a velocity of $50m{s}^{-1}$ towards a stationary observer. The observer measures the frequency of sound as $500Hz$. The apparent frequency of sound as heard by the observer when source is moving away from him with the same speed is (Speed of sound at room temperature $350m{s}^{-1}$)

• A. $400Hz$
• B. $666Hz$
• C. $375Hz$
• D. $177.5Hz$

Answer 1

Answer: (C)

$375Hz$

Speed of sound, $v=350$ $m/s$

Speed of source, $v_s=50$ $m/s$

Let the original frequency of the source be $f_o$.

Apparent frequency heard by observer when a source moves towards the stationary observer :

$f^{\prime }=f_o[\frac{v}{v-v_s}]$

$\therefore$ $500=f_o[\frac{350}{350-50}]$ $⟹f_o=428.6$ Hz

Apparent frequency heard by observer when a source moves away from the stationary observer :

$f^{\prime \prime }=f_o[\frac{v}{v+v_s}]$

$\therefore$ $f^{\prime \prime }=428.6[\frac{350}{350+50}]$ $=375$ Hz