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  4. A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground, of frequency nearly: (Speed of sound = 343 m/s)

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Q. A source of sound $A$ emitting waves of frequency $1800\, Hz$ is falling towards ground with a terminal speed $v$. The observer $B$ on the ground directly beneath the source receives waves of frequency $2150\, Hz$. The source A receives waves, reflected from ground, of frequency nearly : (Speed of sound = $343\, m/s$)

JEE MainJEE Main 2014Waves

Solution:

Given $f_A = 1800Hz$
$v_t=v$
$f_B=2150\,Hz$
Reflected wave frequency received by $A, f_A'=?$
Applying doppler’s effect of sound, $f '=\frac{v_{s}f}{v_{s}-v_{t}}$
Here, $v_{t}=v_{s}\left(1-\frac{f_{A}}{f_{B}}\right)=343\left(1-\frac{1800}{2150}\right)$
$v_{t}=55.8372\,m/s$
Now, for the reflected wave,
$\therefore f_{A}'=\left(\frac{v_{s}+v_{t}}{v_{s}-v_{t}}\right)f_{A}$
$=\left(\frac{343+55.83}{343-55.83}\right)\times1800$
$=2499.44\approx2500Hz$