A source of sound of frequency n and a listener approach each other with a velocity equal to (1/20) of velocity of sound. The apparent frequency heard by the listener is

Question

A source of sound of frequency n and a listener approach each other with a velocity equal to (1/20) of velocity of sound. The apparent frequency heard by the listener is (A)  ( (21/19) )n  (B)  ( (20/21) )n  (C)  ( (21/20) )n  (D)  ( (19/20) )n

Tardigrade Admin · Accepted Answer

From Doppler's effect, the perceived frequency

(n^{'})

is given by

n^{'} = (\frac{v + v _{o}}{v - v _{s}}) n

where

:

' is velocity of sound,

v_{o}

of observer and

v_{s}

of source.
Given,

v_{o} = \frac{v}{20}, v_{s} = \frac{v}{20}

n^{'} = (\frac{v + \frac{v}{20}}{v - \frac{v}{20}}) n

∴ n^{'} = n (\frac{21 v}{19 v}) = (\frac{21}{19}) n

Q. A source of sound of frequency n and a listener approach each other with a velocity equal to $\frac{1}{20}$ of velocity of sound. The apparent frequency heard by the listener is

$(\frac{21}{19}) n$

$(\frac{20}{21}) n$

$(\frac{21}{20}) n$

$(\frac{19}{20}) n$

Q. A source of sound of frequency n and a listener approach each other with a velocity equal to 201​ of velocity of sound. The apparent frequency heard by the listener is

(1921​)n

(2120​)n

(2021​)n

(2019​)n

From Doppler's effect, the perceived frequency (n′) is given by n′=(v−vs​v+vo​​)n where : ' is velocity of sound, vo​ of observer and vs​ of source. Given, vo​=20v​,vs​=20v​ n′=(v−20v​v+20v​​)n ∴n′=n(19v21v​)=(1921​)n

Q. A source of sound of frequency n and a listener approach each other with a velocity equal to $\frac{1}{20}$ of velocity of sound. The apparent frequency heard by the listener is

$(\frac{21}{19}) n$

$(\frac{20}{21}) n$

$(\frac{21}{20}) n$

$(\frac{19}{20}) n$