Dopper Effect in Special Relativity

In summary, the conversation discussed the traffic laws on a planet where drivers must stop at a traffic light in the infrared region with a wavelength of 10^-5m or face a fine. A driver claimed to have seen the light in the X-ray region with a wavelength of 10^-10m while passing it, but it was determined that this was impossible due to the speed of the car being approximately 600 times the speed of light. There was also a discussion about the doppler formula and its application to this situation.
  • #1
yukcream
59
0
Suppose there is a planet, the traffic law there is~
car should stop if the traffic light in infrared region,i.e wavelenght ~10^-5m, otherwise the driver will be fined.
There is a driver claimed that he saw the traffic light still in the X-ray region i.e wavelenght ~10^-10m when passing the traffic light so he hadn't violated the law
If possible, what will be the speed of the car~

However, I found it is impossible for the driver to have this dopper shift, as the speed of the car will be about 600c ~

I did in following step:
by the formula of dopper effect for SR
[(1-v/c)/(1+v/c)]^1/2 = L0/L = 10^-5/10^-10where L is the wavelenght
L0/L = 10^5
the RHS value is so large~
so I expand the LHS as:

(0.5 - 0.5V/c) (0.5+ 0.5v/c) than I get the value as v~600c!

What's going wrong, can anyone help me!

yukyuk
 
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  • #2
For one thing, the doppler formula is:
[tex]f = f' \sqrt{\frac{1 + v/c}{1 - v/c}}[/tex]

As far as your expansion, I don't understand what you are doing. (Realize that v/c is not necessarily small compared to 1.)
 
Last edited:
  • #3
f is stand for frequency here I use wavelenght instead~
 
  • #4
yukcream said:
f is stand for frequency here I use wavelenght instead~
You can convert from one to the other: [itex]f = c/\lambda[/itex].
 

1. What is the Doppler Effect in Special Relativity?

The Doppler Effect in Special Relativity is a phenomenon where the frequency and wavelength of light appear to change when observed by an observer in relative motion. This effect is caused by the relative motion between the source of light and the observer, and is a consequence of Einstein's theory of special relativity.

2. How does the Doppler Effect in Special Relativity differ from the classical Doppler Effect?

The classical Doppler Effect is based on the assumption that the observer and the source of light are at rest relative to each other. However, in the special theory of relativity, the observer and the source of light are moving relative to each other. This means that the observed frequency and wavelength of light will be affected not only by the relative motion between the observer and the source, but also by the velocity of light being constant for all observers.

3. What is the equation for calculating the Doppler Effect in Special Relativity?

The equation for calculating the Doppler Effect in Special Relativity is given by:
fobs = f0 √[(1 + β)/(1 - β)]
where fobs is the observed frequency, f0 is the frequency emitted by the source, and β is the relative velocity between the observer and the source, as a fraction of the speed of light.

4. Can the Doppler Effect in Special Relativity be observed in everyday life?

Yes, the Doppler Effect in Special Relativity can be observed in everyday life. For example, when a police car with its siren on passes by, the frequency of the siren will appear to change for an observer standing on the side of the road. This is because the sound waves emitted by the siren are affected by the relative motion between the observer and the police car.

5. What are some applications of the Doppler Effect in Special Relativity?

The Doppler Effect in Special Relativity has many applications in modern technology. It is used in radar systems, where the frequency of radio waves is shifted to detect the velocity of moving objects. It is also used in medical imaging techniques such as Doppler ultrasound, which is used to measure blood flow in the body. Additionally, the Doppler Effect in Special Relativity is used in astronomy to study the motion and properties of celestial objects.

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