# Is there a maximum doppler shift?

• ktoz
In summary: I was thinking more along the lines of if the observer was moving at a speed close to the speed of light, then the shift would be much greater than 1/2 the wavelength.

#### ktoz

I was playing around with a thought experiment where an observer is moving towards a light source at a speed infinitesimally less than C and it seems like, for any given wavelength, the maximum possible Doppler shift is 1/2. for example near infrared light with a wavelength of 800 nm would be doppler shifted to 400 nm if the observer was traveling extremely close to C.

Is that correct? Or are there relativistic effects that would make the shift greater (or less) than 1/2 the wavelength?

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Yes there is a limit to the Doppler shift: it is 100% .

Doppler

ktoz said:
I was playing around with a thought experiment where an observer is moving towards a light source at a speed infinitesimally less than C and it seems like, for any given wavelength, the maximum possible Doppler shift is 1/2. for example near infrared light with a wavelength of 800 nm would be doppler shifted to 400 nm if the observer was traveling extremely close to C.

Is that correct? Or are there relativistic effects that would make the shift greater (or less) than 1/2 the wavelength?

Which Doppler shift formula do you use? What do you mean by Doppler shift in the limits of your question?

bernhard.rothenstein said:
Which Doppler shift formula do you use? What do you mean by Doppler shift in the limits of your question?

I wasn't using a formula, I was approaching it visually by making a sine wave in an Adobe Illustrator and moving the wave in one direction and the observer in the opposite direction at the same speed. In this model, for a 1 hz wave, the observer would see 2 wave cycles pass in one second. That's where I got the doppler shift of either a doubling of frequency or a halving of wavelngth.

If you imagine that both the observer and wave are traveling at C this would seem to indicate an upper maximum to any shift for a given frequency. But of course this doesn't account for relativistic effects (I don't know what effect if any it would have)

doppler shift

ktoz said:
I wasn't using a formula, I was approaching it visually by making a sine wave in an Adobe Illustrator and moving the wave in one direction and the observer in the opposite direction at the same speed. In this model, for a 1 hz wave, the observer would see 2 wave cycles pass in one second. That's where I got the doppler shift of either a doubling of frequency or a halving of wavelngth.

If you imagine that both the observer and wave are traveling at C this would seem to indicate an upper maximum to any shift for a given frequency. But of course this doesn't account for relativistic effects (I don't know what effect if any it would have)
1. Do you consider the classical or the relativistic one. How do you add the velocities?
2. The observer will never move with C.

bernhard.rothenstein said:
1. Do you consider the classical or the relativistic one.

Most likely I'm thinking in classical terms but the question is basically an effort to discover what, if any, relativistic effects occur.

How do you add the velocities?

I don't really add anything, it's just an observation. If you start out with the leading edge of the observer (a square) touching the leading edge of a sine wave, move the square to the right by 1 wavelength and sine wave left by 1 wavelength, the leading edge of the box "observes" two cycles of the wave.

Not really sure how to represent that as an equation.

2. The observer will never move with C.

True, but as the observer approaches C, the number of observed cycles approaches 2 x frequency

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ktoz said:
Is that correct? Or are there relativistic effects that would make the shift greater (or less) than 1/2 the wavelength?

Relativity does modify the standard first-year textbook result.

For the situation you outlined, the correct relativistic expression is

$$\lambda = \lambda_0 \sqrt{\frac{1 - \frac{v}{c}}{1 + \frac{v}{c}}}.$$

This reduces to the standard non-relativistic expression for speeds much smaller than $c.$

doppler

George Jones said:
Relativity does modify the standard first-year textbook result.

For the situation you outlined, the correct relativistic expression is

$$\lambda = \lambda_0 \sqrt{\frac{1 - \frac{v}{c}}{1 + \frac{v}{c}}}.$$

This reduces to the standard non-relativistic expression for speeds much smaller than $c.$

Who is v in the answer you propose taking into account the scenario proposed by the author of the thread.

bernhard.rothenstein said:
Who is v in the answer you propose taking into account the scenario proposed by the author of the thread.

v is the relative speed between the reference frame of the observer and the reference frame of the light source.

George Jones said:
$$\lambda = \lambda_0 \sqrt{\frac{1 - \frac{v}{c}}{1 + \frac{v}{c}}}.$$
if you put v=c in this formula, you have 0 wavelength. that is, approaching c, you would soon be killed, if not disintegrated, by radiation. creepy, since it is due to energy that you yourself spent to gain high speed... interesting form of suicide.

ktoz said:
I was playing around with a thought experiment where an observer is moving towards a light source at a speed infinitesimally less than C and it seems like, for any given wavelength, the maximum possible Doppler shift is 1/2. for example near infrared light with a wavelength of 800 nm would be doppler shifted to 400 nm if the observer was traveling extremely close to C.

Is that correct? Or are there relativistic effects that would make the shift greater (or less) than 1/2 the wavelength?

If you picture a single wave (peak to peak) and imagine the light traveling to the right at C, and yourself traveling to the left at C, you will meet in the middle. To have a shift greater than 1/2 you would have to travel past the half point which means traveling faster than C.

Of course this has nothing to do with relativity, it just explains why 1/2 seems to be the maximum shift.

grounded said:
If you picture a single wave (peak to peak) and imagine the light traveling to the right at C, and yourself traveling to the left at C, you will meet in the middle. To have a shift greater than 1/2 you would have to travel past the half point which means traveling faster than C.

Of course this has nothing to do with relativity, it just explains why 1/2 seems to be the maximum shift.

Huh? There isn't any maximum shift, as other posters have explained.

An emitted frequency of 1 can be redshifted downward by any multiplicative factor greater than zero.

An emitted frequency of 1 can be blueshifted upward by a multiplicative factor that has no upper limit.

## 1. What is a Doppler shift and how does it relate to maximum Doppler shift?

A Doppler shift is the change in frequency of a wave due to the relative motion between the source of the wave and the observer. The maximum Doppler shift refers to the maximum amount that the frequency can change, which occurs when the source and observer are moving directly towards or away from each other.

## 2. Is there a limit to the maximum Doppler shift?

Yes, there is a limit to the maximum Doppler shift. This limit depends on the speed of the source and observer, as well as the speed of the wave itself. In most cases, the maximum Doppler shift is limited to a few times the original frequency.

## 3. How does the maximum Doppler shift affect the perceived frequency of a wave?

The maximum Doppler shift affects the perceived frequency of a wave by either increasing or decreasing it. If the source and observer are moving towards each other, the frequency will increase, and if they are moving away from each other, the frequency will decrease. The closer the source and observer are to each other, the more significant the change in frequency will be.

## 4. What factors can influence the maximum Doppler shift?

The maximum Doppler shift can be influenced by the speed of the source and observer, the speed of the wave, and the angle at which the source and observer are moving towards or away from each other. Additionally, the medium through which the wave is traveling can also affect the maximum Doppler shift.

## 5. Why is the maximum Doppler shift important in scientific research?

The maximum Doppler shift is essential in scientific research because it allows scientists to measure the relative motion between objects and study various phenomena. It is also used in various fields such as astronomy, meteorology, and medical imaging to understand the behavior of waves and their sources. Understanding the maximum Doppler shift can provide valuable insights into the properties of objects and their motion.