A siren emitting a sound of frequency $800 \mathrm{Hz}$ moves away from an observer towards a cliff at a speed of$15 \mathrm{m}{ \mathrm{s}}^{-1}$ . Then, the frequency of sound that the observer hears in the echo reflected from the cliff is? (The Velocity of Sound in air$\left.=330 \mathrm{m}{ \mathrm{s}}^{-1}\right)$

$\text{ Here, frequency of sound emitted by siren, }{v}_0=800 \mathrm{Hz}$

$\text{ Speed of source, }{v}_s=15 \mathrm{m}{ \mathrm{s}}^{-1}$

$\text{ Speed of sound in air, }v=330 \mathrm{m}{ \mathrm{s}}^{-1}$

$Apparent frequency of sound at the cliff = frequency heard by observer=v$

$\text{ Using Doppler's effect of sound }$

$v=\left(\frac{v}{v-v_s}\right)v_0=\frac{330}{330-15}\times 800$

$=\frac{330}{315}\times 800=838.09 \mathrm{Hz}\approx 838 \mathrm{Hz}$