Question

A source of sound is moving with a velocity of $50 \, ms^{-1}$ towards a stationary observer. The observer measures the frequency of sound as $500\, Hz$. 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 $350 \, ms^{-1}$)

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

Answer 1

Answer: (C)

375 Hz

Answer 2

Speed of sound, $v=350\, mg ^{-1}$
Velocity of sound, $v_{s}=50\, ms ^{-1}$
From Doppler's principle,
I st case,
$f' =\frac{v}{v-v_{g}} f$
$500 =\frac{350}{350-50} f \dots$(i)
where, $f=$ frequency of the source
II nd case,
$f'' =\frac{v}{v+v_{s}} f$
$f'' =\frac{350}{350+50} f \dots$(ii)
From Eqs. (i) and (ii), we get
$\frac{f''}{500}=\frac{350 / 400}{350 / 300}=\frac{3}{4}$
$\therefore f''=500 \times \frac{3}{4}=375\, Hz$