Doppler
Shift
Astrophysics
and Cosmology
Longer ,
lower f
Shorter ,
higher f
The Wavelengths get “squished” in the direction of motion, and
“stretched” in the opposite direction.
Doppler
Shift
Astrophysics
and Cosmology
Longer ,
lower f
Shorter ,
higher f
In the visible spectrum, the color red is associated with the longer
wavelength end of the visible window. The stretching of the wave to a
longer wavelength is called a “red shift”
Doppler
Shift
Astrophysics
and Cosmology
Longer ,
lower f
Shorter ,
higher f
In the visible spectrum, the color blue is associated with the longer
wavelength end of the visible window. The shortening of the wave to a
shorter wavelength is called a “blue shift”
Doppler
Shift
Astrophysics
and Cosmology
A train moves toward an observer at a speed of 25 m/sec. It blows its whistle, and also has
it’s front light on. The observer hears the whistle and sees the light. The wavelength of the
sound wave emitted is .3 meters and the speed of sound is 343 m/sec, and the wavelength of
the light is 500 nm.
What is the Doppler shifted wavelength of the sound wave?
The Doppler shifted wavelength is given by
Apparent Wavelength
True Wavelength
= 1+
Velocity of Source
Wave Speed
Since the train is moving toward the observer, the velocity of the source is negative.
Therefore, for the sound wave
λApparent / λTrue = λApparent / .3 m = 1 – (25 m/sec / 343 m/sec)
→ λApparent = (.92) (.3 m) = .278 m.
This is an 8% shift in the wavelength of the sound wave, which would be noticeable.
Doppler
Shift
Astrophysics
and Cosmology
A train moves toward an observer at a speed of 25 m/sec. It blows its whistle, and also has
it’s front light on. The observer hears the whistle and sees the light. The wavelength of the
sound wave emitted is .3 meters and the speed of sound is 343 m/sec, and the wavelength of
the light is 500 nm.
What is the frequency of the sound wave produced by the source?
What is the frequency of the Doppler shifted sound wave?
Using data from the previous slide
For the wave at the source,
f = v/λTrue = (343 m/sec) / (0.3 m) = 1,143 Hz.
For the Doppler Shifted wave,
f = v/λApparent = (343 m/sec) / (0.278 m) = 1,234 Hz.
Doppler
Shift
Astrophysics
and Cosmology
A train moves toward an observer at a speed of 25 m/sec. It blows its whistle, and also has
it’s front light on. The observer hears the whistle and sees the light. The wavelength of the
sound wave emitted is .3 meters and the speed of sound is 343 m/sec, and the wavelength of
the light is 500 nm.
What is the Doppler shifted wavelength of the light?
The Doppler shifted wavelength is given by
Apparent Wavelength
True Wavelength
= 1+
Velocity of Source
Wave Speed
Since the train is moving toward the observer, the velocity of the source is negative.
Therefore, for the light,
AλApparent / λTrue = λApparent / 500 x 10-9 m = 1 – (25 m/sec / 3 x 108 m/sec)
→ λApparent ≈ 500 x 10-9 m.
The shift is so small for light, the change in wavelength would not be noticeable.
Doppler
Shift
Astrophysics
and Cosmology
A train moves toward an observer at a speed of 25 m/sec. It blows its whistle, and also has
it’s front light on. The observer hears the whistle and sees the light. The wavelength of the
sound wave emitted is .3 meters and the speed of sound is 343 m/sec, and the wavelength of
the light is 500 nm.
What is the frequency of the light wave produced by the source?
What is the frequency of the Doppler shifted light wave?
Using data from the previous slide
For the wave at the source,
f = c/λTrue = (3 x 108 m/sec) / (500 x 10-9 m) = 6 x 1014 Hz.
For the Doppler Shifted wave,
f = c/λApparent ≈ (3 x 108 m/sec) / (500 x 10-9 m) = 6 x 1014 Hz.
Because the Doppler shift is such a small effect for the light, the change in frequenci is
insignificant.
Doppler
Shift
Astrophysics
and Cosmology
A train moves toward an observer at a speed of 25 m/sec. It blows its whistle, and also has
it’s front light on. The observer hears the whistle and sees the light. The wavelength of the
sound wave emitted is .3 meters and the speed of sound is 343 m/sec, and the wavelength of
the light is 500 nm.
What is the Doppler shifted wavelength of the sound wave?
What is the Doppler shifted wavelength of the light?
The Doppler shifted wavelengths are given by
Apparent Wavelength
True Wavelength
= 1+
Velocity of Source
Wave Speed
In order for a Doppler shift to me noticeable, the speed of the source must be comparable
to the speed of the wave.
Sound waves do not travel very fast, and therefore Doppler shifts for sound waves are
quite noticeable for fast moving cars or trains.
Since EM waves move so fast, objects on the earth cannot move fast enough to produce a
noticeable Doppler shift in EM waves. Astronomical objects can, in fact, move at speeds
high enough to detect a Doppler Shift in EM waves.