Special Relativity - Light wave crest

1. Oct 14, 2009

2x2lcallingcq

1. The problem statement, all variables and given/known data
Assume that the speed of light is 3.0m/s - an observer S observes a series of spherical light waves emanating from their fixed origin at time t=0 according to S. The wavelength of the light as seen by S is 1.0m. Another reference frame S' is moving in the positive x-direction of S at a speed of 2.8m. The clocks of s and s' are synched at t=o when the origins are also coincident. X' axis of S' is parallel to and moves directly over the X axis of S. The lengths of the axes of both s and s' will be 20 meters long.

calc all the emitted wave crests as seen by S after time t=1.0s has elapsed (According to S) hint- determine the general equation of motion

using Galilean transform. calc the geometrical structure of ALL emitted wave crests seen by S' after t'=2.5s

Using Lorentz transform. calc the ' ' ' structure of ALL emitted wave crests seen by S' after t'=2.5s

2. Relevant equations
Galilean = http://en.wikipedia.org/wiki/Galilean_transformation
Lorentz = http://en.wikipedia.org/wiki/Lorentz_transformation

3. The attempt at a solution
I am not sure how to really apply both galilean and lorentz to this...
i know that for the first question total wave crests = wavelength/distance

2. Oct 14, 2009

gabbagabbahey

Hi 2x2lcallingcq, welcome to PF!

That's an odd assumption to make! Are you sure it doesn't say, "Assume that the speed of light is 3.0 × 108 m/s"?

I am not sure how to really apply both galilean and lorentz to this...
i know that for the first question total wave crests = wavelength/distance[/QUOTE]

Well, if you can calculate the wavelength and distance in S' using Galilean/Lorentz transformations, then surely you can calculate the number of wavecrests in S', right?

But, you'll need to be careful; the wavefronts are spherical, but the motion is only in the x-direction. What happens to each component of the wavevector? How is the wavelength related to these components?

3. Oct 14, 2009

2x2lcallingcq

I know it is goofy to think of light being so slow - but if that were true... when I walk by you I would be contracting at an alarming rate!

4. Oct 14, 2009

2x2lcallingcq

ALSO i should have mentioned that the only direction that is being measured is in the X and Y direction not the Z

5. Oct 14, 2009

2x2lcallingcq

Also how could i go about using the amazing transformations to accomplish this? I don't exactly know how to use the reference frames for waves of light... I could do it if i were measuring boxes or points on a plain but ....

6. Oct 14, 2009

gabbagabbahey

Are you familiar with the general equation of a plane wave?

7. Oct 14, 2009

2x2lcallingcq

Like the y= cos((wt-k)(r+not)) that kind, ehhh? :)

8. Oct 14, 2009

gabbagabbahey

Sort of, but you are looking for an equation for the electric (or magnetic) field $\textbf{E}(\textbf{r},t)$....look up "electromagnetic plane wave" in your text or on wikipedia...