# Episode 702: Red shift

Changes in wavelength of spectral lines allow us to determine the motion of astronomical objects relative to ourselves.

Summary

• Discussion: Red shift (10 minutes)
• Discussion: The Doppler effect (10 minutes)
• Demonstration: Doppler effect for sound (20 minutes)
• Demonstration: Doppler effect with microwaves (20 minutes)
• Discussion: Speed and frequency (10 minutes)
• Student questions: Binary stars (20 minutes)

Discussion: Red shift
The wavelengths of spectral lines emitted by atoms in an astronomical object are often increased compared to a similar source in the laboratory. We see the same pattern of lines (so we can recognise the elements from which they arise), but the whole pattern is shifted to longer wavelengths. The colour is not necessarily actually red, or even visible. Red shift simply means an increase or shift to a longer wavelength. (For visible light, this means towards the red end of the spectrum.)

There are two distinct explanations: the Doppler effect (due to relative motion of source and observer) and the Cosmological Red Shift (due to the expansion of space).

Both effects result in the same formula for calculating speed v of the object emitting the light.

Discussion: The Doppler effect
The Doppler effect is common to all types of wave motion. It is characteristic of a wave that:

• its frequency depends on its source
• its velocity depends on the medium through which it moves. (Its velocity is not affected by the motion of the source.)
• it is the wave’s wavelength that is affected by relative motion

Demonstration: Doppler effect for sound
Show the Doppler effect for sound using a whirling loudspeaker.

When approaching you (the detector), the crests bunch up as the source is catching up with the wave; l gets smaller, so f gets larger because fl is a constant c, i.e. pitch rises.

Travelling away from the detector, source gets away from the wave, crests stretched out and the pitch drops.

Episode 702-1: The Doppler effect (Word, 27 KB)

Demonstration: Doppler effect with microwaves
You can show the Doppler effect for microwaves reflected by a moving barrier.

Episode 702-2: Doppler shift using microwaves (Word, 34 KB)

Discussion: Speed and frequency
Derive the relationship Dl / l = Df / f = v / c. This says that the fractional change in wavelength or frequency is equal to the ratio of the speed of the source to the speed of light.

Episode 702-3: Doppler derivation for light (Word, 23 KB)

Episode 702-4: The Doppler shift (Word, 45 KB)

The consequence is that the frequencies of spectral lines change in proportion. NB many text books have diagrams that do not really show the increasing separation of spectral lines with wavelength, as though all the lines in a spectrum were shifted by an equal amount rather than by an equal fraction. The diagram above shows the correct version.

An interesting example: the Sun rotates, and its light is therefore Doppler shifted. The radiation from the side approaching the Earth is blue shifted; the radiation from the side moving away from the Earth is red shifted. The speed of rotation can be determined from these frequency shifts.

Episode 702-5: Doppler shifts from part of a galaxy (Word, 61 KB)

Student questions: Binary stars
When two stars orbit about one another, one may be moving towards us (blue shift), and the other away (red shift).

Episode 702-6: Binary stars (Word, 61 KB)