Understanding the Time Offset in EM Plane Waves

[maxsthekat]

This isn't a homework question so much as a general question about the equation I see used in the textbook:

The E field of an EM wave is defined as E(x, y, z, t) = E₀sin(kx - wt)y_hat and the B field of an EM wave is defined as B(x, y, z, t) = B₀sin(kx - wt)z_hat.

Why is there a minus sign in front of the wt term? I understand how kx (the offset in space) is positive; why wouldn't the time offset (wt) also be positive in this equation?

Thanks!

-Max

 

[Redbelly98]

The minus sign just means the wave is traveling in the +x direction.

You could have it be +wt. In that case the wave travels in the -x direction.

 

[maxsthekat]

I see... But, why is a +x direction a -wt term?

 

[rootX]

At t = 0
. f(k). .........

At t = t
..... f(k-wt) .....

Where f(k) is a pulse

see f(x-5) goes towards positive side and f (x+5) is at negative side or you can use the word "shift". This can understood good if you use one simple pulse rather than a complex sinusoidal function

 

[Redbelly98]

I see... But, why is a +x direction a -wt term?

Hmmm. Well, let me ask a somewhat more basic question. Do you understand why a graph of the function f(x-1) would look the same as f(x), except that it would be shifted by 1 unit in the +x direction?