What is Doppler effect? Obtain an expression for the apparent frequency of sound heard when the source is in motion with respect to an observer at rest?
Answers
Explanation:
Formula used:
f=vλorλ=vff=vλorλ=vf
Where
ff
is the frequency,
λλ
is wavelength and
vv
is the velocity of the sound wave.
Complete step by step answer:
Given Data: -
Let us suppose a source of sound
SS
is emitting sound waves of frequency
ff
. These waves are traveling in the medium with velocity
vv
. The observer is at rest.
Doppler Effect: -
It is defined as the phenomena of apparent change in frequency of sound due to relative motion between the source of the sound and observed.
From the above given condition there may be two cases
Case 1:
When the source is moving with velocity
vsvs
towards the observer at rest then,
the relative velocity of sound waves reaching to the observer
=v−vs=v−vs
now the apparent wavelength will be as follows:
λ′=v−vsfλ′=v−vsf
so, the apparent frequency is as follows
⇒f′=vλ′=vv−vs/f⇒f′=vλ′=vv−vs/f
⇒f′=vv−vsf⇒f′=vv−vsf
Case 2:
When the source is moving with velocity
vsvs
away from the observer at rest then,
the relative velocity of sound waves reaching to the observer
f′=vv+vsff′=vv+vsf.
verify.