# Please explain Dopler effect of light

1. Dec 24, 2011

### thetexan

How can there be any shifting of light frequency due to dopler effect? Frequency is just a fancy way of stating 'wave' or, as depicted on all explanitory diagrams, a sinusoidal wave. Each cycle of the wave represents one part of the total waves measured in a given amount of time which is the frequency of the light. To have a dopler effect the waves must either arrive farther apart or closer together than they were when they were originated. If the speed of light is universal how can there be a difference?

If the star were to blink on then off for one second you would have one second's worth of light coming from the point of origin. This would be a measurable, distinct and determinable length based on the speed of light. Within this length would be a fixed number of waves. The front of the main group of waves arrives at earth at the speed of light as does the back of the main group. Doesnt each wave within the group also arrive at that same speed? If this is true then the only other factor would be that the entire length of the main group of 1 second's worth of light is longer at arrival than when it left.

But if light speed is universal how can there be any lengthening?

tex

2. Dec 24, 2011

### zhermes

See: Special Relativity

While frequency is universally a proper of a wave, it is certainly not synonymous with 'wave'---and applies to any type of wave (sinusoidal or otherwise).
Frequency is the rate at which a wave oscillates, which is not the same thing as the wave's velocity. The simplest way to measure or describe frequency, is to count the number of wave-crests (or any repeating element) which pass by a given point, in a given amount of time. The frequency is related to the velocity by the equation $$v = \nu \lambda$$.

Good point, and good question. While the speed of light is constant, the other 2 elements of the above equation are not: the frequency (the inverse of the 'period' or duration for a single oscillation), and the wavelength (length of the wave) are both not constant, because of special relativity (for example).
As the special relativity article (linked above) explains, an observer at rest will measure a different length and different time duration than another observer at a constant velocity with respect to the first. There are also other (similar) causes of doppler effects.

If the star 'measures' one second during which it is 'on', a moving observer would measure a longer duration of time. Similarly, if the star 'measures' the wave traveling 1 light year before it is measured; a moving observer would measure a shorter distance. These two effects conspire together to make the product of the frequency and the wavelength constant---the speed of light.

3. Dec 24, 2011

### Janus

Staff Emeritus
Consider the following animations. The first shows waves of light emitted by a source stationary to the two dots. The waves expand out as circles from the source.

The second shows what happens if the source moves. The waves still expand out as circles from the point of emission, but now, between the emission of the front of the wave to the back of the wave, the source has moved closer to the blue dot and further from the Red dot. Since the ends of the waves travel at c and the back of the wave has a shorter distance to travel, it takes a shorter time to reach the blue dot (and conversely, a longer time to reach the Red). Thus, to the blue observer, the wave is compressed and the for the red observer, it is stretched out. All without the speed of light changing at all.

4. Dec 24, 2011

### thetexan

Well, this is what I understand. Please tell me if Im correct.

A star, very far away, blinks on then off sending out a 7 cycle burst of light(the center image)...at the speed of light.

It arrives, after billions of years of travel, at the earth which, due to expansion, is receding from the star at a very great rate of speed. Due to the observer's speed the original burst is elongated, or appears so, which causes the entire 7 cycle burst to arrive at a lower frequency thus causing the redish color. If there were a situation where we were getting closer to a star the bottom image would be the case and the star would seem blueish. This stretching of the waves is what is refered to as Dopler. Is that right?

tex

5. Dec 24, 2011

### Bobbywhy

Wonderfully clear animations of the Doppler Effect! Thanks, Janus.

6. Dec 24, 2011

### Staff: Mentor

Without going in depth, yes.

However, there is a critical piece or two that you are missing here. The standard picture of a light wave being 1 or 2 squiggly lines is NOT what light is. The up and downs of that picture represent a shift from positive to negative and back to positive of the lights electric and magnetic fields. Your statement, "A star emits a 7 cycle burst..." is not what happens. Light is only emitted or absorbed in discrete quanta called Photons. In spite of this, it still behaves extremely similar to any other wave, such as a water or sound wave, and does in fact exhibit doppler shift.

Another problem is that frequency shift due to the expansion of space is similar to, but not exactly like the Doppler Effect. (At least to my knowledge) As far as I know the expansion of space actually "stretches" out the light wave as it travels, resulting in a frequency shift. Whether there is any technical difference between the two is beyond me.

7. Dec 29, 2011