Need some help with Doppler effect problem Exam Monday

[Linda]

Hi everyone,

really would love it if someone could help me with this. I think it's probably a very easy problem, only I can't seem to find the right formlula, or understand the only one I found...

This is the problem:

I'm in my car, driving towards a crossing with a red traffic light (lambda = 700 nm). How fast do I need to drive to make the traffic light appear green (lambda = 500 nm) to me?

(I suppose this must have to do with the Doppler effect, but the only formula I can find on it says: v/c = (lambda - lambda0) / lambda0

v = speed of the source of radiation, c = speed of light, lambda = measured wavelength, lambda0 = something that strictly translated from Swedish to English means "resting" wavelength, don't know if that makes any sense? I just have no idea what lambda0 is!?)

Hope I explained it ok! Does anyone have any suggestions on how to solve this problem?

Thanks,
Linda, Sweden

 

[Galileo]

The formula for the Doppler effect for light is:

[tex]\frac{\lambda'}{\lambda}=\sqrt{\frac{1-v/c}{1+v/c}}[/tex]
where [itex]\lambda'[/itex] is the Doppler-shifted wavelenght and [itex]v[/itex] is the relative velocity between source and observer. (v is positive if they are approaching each other)

For v<<c, this equation is approximated by
[tex]\frac{\lambda'}{\lambda}=1-\frac{v}{c}[/tex]

You know the wavelenghts, so you can solve for v.

 

[Linda]

Thanks a lot for that!
Was easy to solve with your help , now let's hope I pass my exam tomorrow as well!
Thanks again,
Linda, Sweden

 

[chinmayrshah]

I want to ask that will this phenomenon hold true for a celestial object like sun? Does Doppler Effect hold true also for the stationary light source? I mean, that if you are traveling to the signal (in above problem) with velocity Vp (19.44m/s) and the velocity of signal light is Vs (3x10^8 m/s) and if you apply the relative velocity concept, it gives:

Vr = Vp + Vr (In case of making the light source at 0 velocity)
= 300000019.44 m/s (Speed of object??)
OR
Vr = Vp - Vr (In case the observer is stationary)
= 299999980.56 m/s (Speed of light??)

Do clear this to me. I know there can be my misconception but please help me to solve this!
Thanks in advance
:)

 

[asteriatic]

Hi Linda,

Thank you for reaching out for help with your Doppler effect problem. The formula you found is indeed the correct one to use in this situation. Lambda0, or "resting" wavelength, refers to the wavelength of the source of radiation (in this case, the traffic light) when it is at rest.

In order to solve the problem, you will need to rearrange the formula to solve for v, the speed of the source of radiation. This can be done by multiplying both sides of the equation by c and then rearranging the terms. Once you have solved for v, you can plug in the values for lambda (500 nm) and lambda0 (700 nm) to find the speed at which you need to drive.

I hope this helps and good luck on your exam!

Best,