1. Astrophysics and Cosmology The Wavelengths get “squished” in the direction of motion, and “stretched” in the opposite direction. Doppler Shift Longer, lower f Shorter, higher f

2. Astrophysics and Cosmology Doppler Shift 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”

3. Astrophysics and Cosmology Doppler Shift 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”

4. Astrophysics and Cosmology Doppler Shift Apparent Wavelength True Wavelength Velocity of Source Wave Speed =1 + Since the train is moving toward the observer, the velocity of the source is negative. Therefore, for the sound wave λ Apparent / λ True = λ Apparent /.3 m = 1 – (25 m/sec / 343 m/sec) → λ Apparent = (.92) (.3 m) =.278 m. This is an 8% shift in the wavelength of the sound wave, which would be noticeable. 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

5. Astrophysics and Cosmology Doppler Shift Using data from the previous slide For the wave at the source, f = v/λ True = (343 m/sec) / (0.3 m) = 1,143 Hz. For the Doppler Shifted wave, f = v/λ Apparent = (343 m/sec) / (0.278 m) = 1,234 Hz. 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?

6. Astrophysics and Cosmology Doppler Shift Apparent Wavelength True Wavelength Velocity of Source Wave Speed =1 + Since the train is moving toward the observer, the velocity of the source is negative. Therefore, for the light, Aλ Apparent / λ True = λ Apparent / 500 x 10 -9 m = 1 – (25 m/sec / 3 x 10 8 m/sec) → λ Apparent ≈ 500 x 10 -9 m. The shift is so small for light, the change in wavelength would not be noticeable. 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

7. Astrophysics and Cosmology Doppler Shift Using data from the previous slide For the wave at the source, f = c/λ True = (3 x 10 8 m/sec) / (500 x 10 -9 m) = 6 x 10 14 Hz. For the Doppler Shifted wave, f = c/λ Apparent ≈ (3 x 10 8 m/sec) / (500 x 10 -9 m) = 6 x 10 14 Hz. Because the Doppler shift is such a small effect for the light, the change in frequenci is insignificant. 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?

8. Astrophysics and Cosmology Doppler Shift Apparent Wavelength True Wavelength Velocity of Source Wave Speed =1 + 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. 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