Special Relativity - Light wave crest

[2x2lcallingcq]

Homework Statement

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

Homework Equations

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

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

 

[gabbagabbahey]

Hi 2x2lcallingcq, welcome to PF!

Assume that the speed of light is 3.0m/s[/color]

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?

 

[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!

 

[2x2lcallingcq]

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

 

[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 ...

 

[gabbagabbahey]

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

 

[2x2lcallingcq]

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

 

[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...