A siren emitting a sound of frequency $800\,\, Hz$ moves away from an observer towards a cliff at a speed of $15 \,\,m s^{-1}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is .... $Hz$
(Take velocity of sound in air $= 330\,\, m s^{-1}$)
(Take velocity of sound in air $= 330\,\, m s^{-1}$)
NEET 2016, Medium
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Here, frequency of sound emitted by siren,
$v_{0}=800 \mathrm{Hz}$
Speed of source, $v_{s}=15 \mathrm{m} / \mathrm{s}$
Speed of sound in air, $\mathrm{v}=330 \mathrm{m} / \mathrm{s}$
Apparent frequency of sound at the cliff $=$ Frequency heard by observer $=v$
Using Doppler's effect of sound
$v=\left(\frac{v}{v-v_{S}}\right) v_{0}=\frac{330}{330-15} \times 800$
$=\frac{330}{315} \times 800=838.09 \mathrm{Hz} \approx 838 \mathrm{Hz}$
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