[Jonathan Robbins]

Jonathan Robbins  asked the Naked Scientists:
   
Hi Chris,
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I was wondering if the Doppler effect applies to all waves of the electromagnetic spectrum, and in particular, light.   For example would there be a colour shift apparent on an object moving toward or away from an observer?   If so, how fast would an object need to be moving in order to completely change colour say from red to orange?
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If the Doppler effect does apply to light and other parts of the electromagnetic spectrum, can we expect to be able to shift a wave type to another wave type (say microwaves to x-rays) simply by accelerating the wave emitter to a high speed? Presumably if this was the case, the amount of shift up the spectrum would be capped when the emitter reached the speed of light (ignoring the implausibility of this) so how much shift would this allow?
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Sorry if this is a heavy one but I'm fascinated to know.
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Thanks!
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Jon, Isle of Wight

What do you think?

[lightarrow]

Yes.

The formula is:

λ' = λ*Sqrt[(c - v)/(c + v)]

λ = wavelenght of the source when it doesn't move with respect to the detector/observer.

λ' = wavelenght of the source when it moves with respect to the detector/observer.

v = velocity of the source with respect to detector/observer; positive if the source is approaching to observer (or the observer is approaching the source, of course is the same).

If you want to find the velocity v knowing the rate λ'/λ:

(v/c) = [1 - (λ'/λ)²]/[1 + (λ'/λ)²].

If you want red to become blue, let's say red with λ = 660nm = 6.6*10^-7m, to blue with λ' = 440nm = 4.4*10^-7m, you have λ'/λ = 4.4/6.6 = 2/3 and so:

(v/c) = [1 - (2/3)²]/[1 + (2/3)²] = 5/13, so v ≈ 0.385c.


If instead you want microwaves to become X rays, let's say microwaves with λ = 1mm = 10^-3m, to X rays with λ = 10nm = 10^-8m, you have λ'/λ = 10^-8/10^-3 = 10^-5 and so:

(v/c) = [1 - (10^-5)²]/[1 + (10^-5)²] ≈ 0,9999999998  -->  v = 0,9999999998c.

Edit. Soul surfer reminded me this: of course the above formulas hold even when v is negative, that is the source recedes from observer. Then λ' increases (doppler red shift of galaxies, for example)

[Soul Surfer]

There is absolutely no limit to the amount of red and blue shifting that can take place for example the cosmic microwave background radiation was visible light when it set off and microwaves are regularly changed to xrays in the lab using synchrotron radiation sources

[Bored chemist]

The doppler effect has been verified experimentally from the gamma ray region to the microwave region. Possibly further- I don't know.
It's fair to say that the answer is "yes it can".

[HankRearden]

thats a really cool concept, I've never really thought of the doppler effect in any context except that of sound.

[lyner]

Doppler Radar is used by 'the Plod'  I believe?

[krytie75]

Hello.

I'm the original poster, and signed up to this forum because of the amazing answer(s) I received.  Thanks to everyone for their contributions.

I do have a few further questions that expand on this theme though.  Firstly, what's the maximum possible shift up/down the spectrum, based on the maximum speed of the emitter?  For example, how far up the spectrum would you be able to shift a 10Khz soundwave if the emitter (speaker) was travelling at the universal maximum speed of light (c)? If this is not possible, what's the limiting factor, and how far can it go?  Apologies if this can be worked out from the formula provided above.

Secondly, I was under the impression that visible light is the only part of the spectrum which is/can be a particle (the photon) as well as a wave.  If this is the case, how could a simple sound wave be doppler shifted to appear as light where sound has no particle?  Alternatively, if light was doppler shifted to microwaves, what would happen to the particle (considering the wave is still being transmitted with/as a particle).

I have a few more questions about this but will hold off posting them until we get some info on these ones.

Thanks again,

Jon

[Soul Surfer]

krytie75   You are making a fundamental mistake by mixing up sound and light.  They are both waves but in different media with different properties.  Most of the discussions here refer only to light.  Sound is a pressure wave that travels through a medium and objects can move father than the velocity of sound when the wave gets totally compressed into what is called a shock wave.

The same thing  can happen with light when particles that are travelling faster than the speed of light in a medium (like glass)  enter the medium and create what is known as Cerenkov radiation.

All electromagnetic radiation from radio waves to gamma rays exhibits a wave particle duality but the particle properties of waves much longer than infra red are very difficult to observe.

[krytie75]

Soul Surfer - Ah I see the mistake I made.  Sound waves do not form part of the electromagnetic spectrum.  Thanks for pointing this out.