Doppler effect - can't imagine how the frequency of light can change

[musicgold]

TL;DR Summary

I am familiar with the Doppler effect in the case of sound waves (the train whistle example). But what is bugging me is the Redshift phenomenon in Astronomy and the apparent change in the frequency (wavelength) of the light.

AM/FM radio stations, cell phone towers transmit signals at certain frequencies. How can the frequency of a signal change depedning on whether the receiver is moving towards or away from the source?

I thought that the frequency of an electromagnatic wave is determined at the source (the energy carried by its photons, reflects the frequency). My intution is not able to swallow the fact that it changes if the source is moving away from us.

Is there any other way to intutively grasp this phenomenon?

Thanks

 

[lomidrevo]

How can the frequency of a signal change depedning on whether the receiver is moving towards or away from the source?

Because frequency is frame dependent, it is not an invariant quantity.

I thought that the frequency of an electromagnatic wave is determined at the source (the energy carried by its photons, reflects the frequency). My intution is not able to swallow the fact that it changes if the source is moving away from us.

As frequency depends on the frame of reference, only an observer at rest with respect to the source would measure the frequency "native" to the source.

Maybe a helpful analogy: kinetic energy of body also depends on the observer. At the rest frame of the body it would be always 0, but it would depend on the relative velocity otherwise. Does that bugging you?

 

[PeroK]

My intution is not able to swallow the fact that it changes if the source is moving away from us.

Is there any other way to intutively grasp this phenomenon?

Any oscillating wave will decrease in frequency if the source moves away from you. You can see this with a simple diagram. The frequency for a) someone moving with the source and b) someone not moving with the source must be different. How could they be the same?

 

[Ibix]

My intution is not able to swallow the fact that it changes

Put a source of EM waves and a detector on a bench. Put another detector on a cart and let it move away from the source. Say that the cart detector passes the bench detector just as a wave crest arrives. By the time the next crest arrives at the bench detector, though, the cart detector has moved, and hence it receives the crest later. Thus it sees a longer period and lower frequency.

As PeroK noted, nothing about the analysis of that experiment changes if I replace "EM" with any other kind of wave.

I thought that the frequency of an electromagnatic wave is determined at the source (the energy carried by its photons, reflects the frequency).

Not quite. $E=h\nu$, sure, but energy is frame dependent. Are you sitting down? Would you say your kinetic energy is zero? But an observer hovering at rest with respect to the Earth would say you are doing (depending on latitude) up to 1,000mph. And one at rest with respect to the Sun would say you were doing nearly 20km/s. "How much energy you have" depends who is doing the measuring.

A quantity called the energy-momentum four vector is agreed on by all frames, but how you derive energy from that is frame dependent.

 

[Klystron]

Summary:: I am familiar with the Doppler effect in the case of sound waves (the train whistle example). But what is bugging me is the Redshift phenomenon in Astronomy and the apparent change in the frequency (wavelength) of the light.

AM/FM radio stations, cell phone towers transmit signals at certain frequencies. How can the frequency of a signal change depending on whether the receiver is moving towards or away from the source?

I thought that the frequency of an electromagnetic wave is determined at the source (the energy carried by its photons, reflects the frequency). My intuition is not able to swallow the fact that it changes if the source is moving away from us.

Is there any other way to intuitively grasp this phenomenon?

Thanks

Since you understand Doppler shift of acoustic waves but intuition fails you in understanding red shift of EM waves, consider an analogy. A loud siren on a speeding vehicle drops in pitch as the vehicle departs according to listeners on the ground while the vehicle driver hears the unchanged natural frequency of the siren.

Consider an EM source (emitter) on a spacecraft departing from Earth, say a continuous wave radar transmitter broadcasting at a set frequency f_t detected by your antenna back on Earth. Ignore the Earth's motions for the sake of comparison to the departing vehicle with the loud siren. The radar on the departing craft remains on frequency but you detect lower frequency toward the 'red end' of the EM spectrum as the spacecraft carries the EM source away from your antenna.

To the stationary observer the pitch of the siren appears to lower as the vehicle departs. To the stationary radar receiver the EM source shifts to a lower frequency 'toward the red' as the emitter rapidly recedes. Red shift is itself an analogy to the visible portion of the EM spectrum where humans see longer wavelengths (lower frequencies) as red and higher visible light frequencies (shorter wavelengths) as blue.

Your sensitive radar receiver detects this lengthening of the expected wavelength (lower frequency) and can use this comparative data to determine that the source is receding and even estimate the recession rate in the radial direction. This explanation of the Doppler effect begs the question: How can radar operate on moving targets with the expected frequency shifting as the target moves?

Some radars emit RF in pulses with information coded or modulated into each discrete pulse. The receiver recognizes the unique pulse pattern despite the distorting effects of relative motion. Doppler radars embrace 'red shift' and 'blue shift' to detect and determine target motions.

 

[sophiecentaur]

@musicgold
It would be a good idea if you responded to some of the above so that we can know how well we're doing in the attempt to help you. You say that you understand the concept of Doppler shift but what's your perceived difference between the effect with sound and the effect with EM waves (apart from the numbers involved)? Bearing in mind that Doppler in EM waves happens at speeds well below c*, the two waves can be thought of as equivalent. (There is a 'modified Doppler' equation that kicks in near c but that's something to deal with later).
*The Mössbauer effect can allow us to detect speeds of a few mm/s. (It's a simple experiment that was on my basic Degree Physics course)

 

[Speady]

The mystery is simply solved: whether the speed of light is invariant, or the wavelength is invariant. The former has been chosen. It's an assumption. The assumption could just as well have been that the wavelength is invariant and the speed of light is not. It really doesn't matter what you choose: the result of both assumptions is equivalent. For people who doubt this, I have this question: At what speed does light from a galaxy 20 billion light years away come towards us?

 

[Ibix]

The mystery is simply solved: whether the speed of light is invariant, or the wavelength is invariant. The former has been chosen. It's an assumption.

No it isn't. The frame invariance of the speed of light is well established both experimentally and theoretically.

At what speed does light from a galaxy 20 billion light years away come towards us?

$c$, in any physically meaningful sense. You can certainly pick coordinate systems where the coordinate speed of light is not $c$ (edit: which is what people are doing when they talk about galaxies receding faster than light), but that has nothing to do with Doppler shift or invariance of anything.

 

[Dale]

the result of both assumptions is equivalent

I don’t think this is at all correct. Do you have a professional scientific reference that makes this claim?

 

[mitochan]

$$\nu'=\nu\frac{\sqrt{1-\frac{v^2}{c^2}}}{1-\cos\theta \frac{v}{c}}$$
where $\theta$ is angle between light propagation and the motion.
For $\theta$=0
$$\nu'=\nu\frac {\sqrt{1+\frac{v}{c}}} { \sqrt{1- \frac{v}{c}} }$$
When you drive a car of 160km/h listening AM radio of 1MHz
$$\frac{v}{c}=1.5E-7$$
$$\nu'=1000000.15Hz$$
I think radio engineering can disregard the difference.