1.
RELATIVISTIC
DOPPLER ELECTED
FOR LIGHT
@Asan Fizika @fizika_physics

2.
What do you observe when you throw a pebble into a body of
water? (apart from the pebble sinking). Doppler effect explained
why we perceive a change in frequency when the wave source
approaches or retreats from us...
Doppler effect is the change in frequency of a wave for an
observer moving relative to its source. The observer observes an
upward shift in frequency when the wave source is approaching
and a downward shift in frequency when the wave source is
retreating. Doppler effect applies to all waves including; Sound
waves, Light waves, Water waves.
Doppler effect originated in 1842 by an Austrian physicist
“Christian Doppler”.
He proposed doppler effect in his article “Über das farbige
Licht der Doppelsterne und einiger anderer Gestirne des
Himmels”. Translated as “On the colored light of the binary
stars and some other stars of the heavens”.

3.
The Relativistic Doppler Effect
Suppose an observer in S sees light from a source in S′ moving away
at velocity v. The wavelength of the light could be measured
within S′ — for example, by using a mirror to set up standing waves
and measuring the distance between nodes. These distances are
proper lengths with S′ as their rest frame, and change by a
factor 1 − 𝑣2/𝑐2 when measured in the observer’s frame S, where
the ruler measuring the wavelength in S′ is seen as moving.

4.
(a) When a light wave is emitted by a source fixed in the moving inertial frame S',
the observer in S sees the wavelength measured in S'. to be shorter by a
factor 𝟏 − 𝒗𝟐/𝒄𝟐.
(b) Because the observer sees the source moving away within S, the wave pattern
reaching the observer in S is also stretched by the factor (cΔt+vΔt)/(cΔt)=1+v/c

5.
If the source were stationary in S, the observer would see a length cΔt of the wave
pattern in time Δt. But because of the motion of S' relative to S, considered solely
within S, the observer sees the wave pattern, and therefore the wavelength,
stretched out by a factor of
as illustrated in (b).

6.
where 𝝀𝒔𝒓𝒄 is the wavelength of the light seen by the source in S' and 𝝀𝒐𝒃𝒔 is the
wavelength that the observer detects within S.

7.
Red Shifts and Blue Shifts
The observed wavelength 𝝀𝒐𝒃𝒔 of electromagnetic radiation is longer
(called a “red shift”) than that emitted by the source when the source
moves away from the observer. Similarly, the wavelength is shorter
(called a “blue shift”) when the source moves toward the observer. The
amount of change is determined by

8.
where 𝝀𝒔 is the wavelength in the frame of reference of the
source, and v is the relative velocity of the two
frames S and S′. The velocity v is positive for motion away
from an observer and negative for motion toward an
observer. In terms of source frequency and observed
frequency, this equation can be written as:

9.
Example: Calculating a Doppler Shift
Suppose a galaxy is moving away from Earth at a speed 0.825c.
It emits radio waves with a wavelength of 0.525 m. What wavelength
would we detect on Earth?
Strategy:
Because the galaxy is moving at a relativistic speed, we must determine
the Doppler shift of the radio waves using the relativistic Doppler shift
instead of the classical Doppler shift.

10.
Application of Doppler effect
Doppler effect has found its use in several other area which includes;
Astronomy,
Vibration measurement,
To Sense Gesture (computer base)
Audio
Velocity profile measurement etc.

11.
In the 1600 years or so since Doppler first described the wave phenomenon that
would cement his place in history, several practical applications of the Doppler
effect have emerged to serve society. In all of these applications, the same basic
thing is happening.
One application of Doppler effect found in nature, occurs in bats hunting for their
prey. Bats navigates it’s flight by emitting whistles and listening for the echoes.
When chasing prey, its brain detects a change in pitch between the emitted whistle,
and the echo it receives. This tells the bat the speed of its target, and the bat adjusts
its own speed accordingly.
The Doppler effect is used in some types of radar, to measure the speed of detected
objects. For example a police officer uses radar guns to check for speeding vehicles.
The radar gun emits waves at a particular frequency, which when strikes the
vehicles bounce back toward the gun.
The radar gun then measure the frequency of the returning waves, then eventually
determine the speed.

12.
Reference:
 https://www.youtube.com/watch?v=0EOWEMZHZpI
https://www.youtube.com/watch?v=zpW0MpIOQh0&t=390s
https://byjus.com/physics/doppler-effect/
https://www.youtube.com/watch?v=JJciUSRX74c&t=127s
https://en.wikipedia.org/wiki/Relativistic_Doppler_effect
https://www.youtube.com/watch?v=vDvIhiCnatE

13.
THANK YOU
FOR YOUR
ATTENTION.