Basic Optics Question. (wave front)

[bumclouds]

Homework Statement

E=Emax.sin(ωt-kx) describes the electric field of a monochromatic plane wave traveling in the x-direction. Verify that a plane which is perpendicular to the x-diretion and moves along the x-axis at the same speed as the wave is a wave front.

Homework Equations

E=Emax.sin(ωt-kx)

The Attempt at a Solution

A "wave front" is a surface where the phase is always the same.

-----|-------------------|----------> x-axis
___x1,t1______________x2,t2______

At x1, t2 and x2, t2 must have the same phase which is in the brackets of sin() in "relevant equations".

so...
ωt1-kx1 = ωt1-kx2

and I'm guessing since the speed is the same at both points x1/t1 is equal to x2/t2 and we substitute those in or something?? I don't know I've thought about this a lot and I'm very stuck!

 

[Mentz114]

Here's a hint : the velocity of the wave described is $$\frac{\omega}{k}$$