Doppler shifts

Doppler shifts are part of the phenomenology of waves (here, we treat the light we receive from stars as a wave-like phenomenon). To understand why this is important for planet detection, let us look at the analogous classical Doppler phenomenon. First, consider what happens to a pan full of water if I drop a rock into it (or disturb it in any manner). I would generate a pulse that moves out from the point of disturbance in all directions.

To generate a wave, I would apply a series of periodic disturbances (that is, tap the water once every second). I then get the case to the left. I have set-up a series of outward moving pulses whose crests are separated by equal intervals in space and pass by a given observer at a frequency of 1 crest per second. The distance between the crests is the wavelength of the wave and the the number of crests that pass by per second is the frequency of the wave.

Next, suppose I move the point at which I tap the water. For example, suppose I start tapping the water at the center of the pan but for each successive tap, I move a short distance to the right. This is the case shown to the right.

A series of concentric circular waves moves away from the disturbance.

Circular waves are still produced but the distances between the crests of the waves depends upon where you sit.

For the picture on the left, it doesn't matter where I sit while I watch the wave. Whether I sit on the right, on the left, at the top, or at the bottom, the rate and distance between the passing crests is the same, I see the same wavelength for the wave wherever I sit.

Q: What if I sat on the right hand side of the picture on the right, how would the wavelength I measure compare to the wavelength that I would measure if I sat on the left side of the picture?

The rate is faster and the distance between crests is smaller for the observer on the right than for the observer on the left. We conclude that
if a source of waves approaches the observer, the frequency is increased and the wavelength of the wave is shortened. We say that the wave is blueshifted. If a source of waves runs-away (recedes) from the observer, the wavelength of the wave is stretched, we say that the wave is redshifted. This phenomenon is the Classical Doppler Effect.

Q: How does the size of the Doppler shift depend on the speed that the source is moving?

For the stationary source, the wavelength of the wave was unchanged. For the moving source, the wavelength of wave was changed. It was redshifted or blueshifted depending upon whether the source receded or approached the observer. We can conclude that the effect increases in size as the speed of the source increases. We state without proof, that the actual amount of the shift (the amount of stretching or contraction of the wavelengths) is found by comparing how fast the star moves compared to how fast the wave moves.

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