Relativistic Doppler Effect Formula with Example

Relativistic Doppler Effect Formula :

The Doppler Effect is the effect perceived when energy waves like light waves or sound waves travel with regards to an observer. There will be an alteration in frequency. An upward shift in frequency for an approaching source and a downward shift in frequency in the case of a retreating source.

V’ =V √ 1+v/c /1-v/c

β=v/c then relativistic Doppler effect formula is articulated as

V’ =V √ 1+ β /1- β

Where,
ν’→  Apparent frequency (the frequency of observer)

V→ The Real frequency (frequency of the source)  m/s

The observer’s velocity v is,

C→ speed of light in m /s

For a moving source and a moving observer, the formula of frequency according to Doppler’s effect is given by:

Relativistic Doppler Effect formula F(Hz) in hertz is equal to the velocity of waves in the medium c(m/s) in meter per second and addition of the velocity of the receiver relative to the medium vr(m/s) in meter per second and divided by the velocity of the waves in the medium c(m/s) in meter per second and addition of  the velocity of  source relative to the medium vs(m/s) in meter per second and multiply the  frequency of waves in the medium F(Hz) in hertz. Hence the Relative Doppler effect formula can be written as

F(Hz)=(c(m/s)+vr(m/s) /c(m/s)+ vs(m/s))* f0(Hz)

F→ frequency of waves in the medium in Hz

c → velocity of waves in the medium in m/s

Vr​ → velocity of the receiver relative to the medium in m/s

Vs​→ velocity of the source relative to the medium in m/s

Sample Problems :

Example 1 :

calculate the apparent frequency heard by the observer, if the velocity of sound is 540 m/s? In a source is moving towards observer with a speed of 30 m/s and having frequency 340 Hz and observer is moving towards the source with a velocity of 30 m/s.

Solution :

Vs=30 m/s

Vr=30 m/s

C=540Hz

F0=340Hz

F=(c+vr) (c+Vs) F0

F=(540-30)/(540+30) *340

F=304.210Hz

Example 2 :

Calculate the apparent frequency heard by the observer, if the velocity of sound is 600m/s? In a source is moving towards observer with a speed of 50m/s and having frequency 400  Hz and observer is moving towards the source with a velocity of 50m/s.

Solution :

Vs=50 m/s

Vr=50 m/s

C=600Hz

F0=400Hz

F=(c+vr) (c+Vs) F0

F=(600-50)/(600+50) *400

F=338.46Hz

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