How Do You Sketch a Traveling Wave at Different Time Intervals?

[stawbeegirl]

hi everyone,
i am stuck working on this problem and thought i'd post it to the forum

if an electric field wave is given by E = 50cos(10^8*t + k*z)

what does the wave look like at t=0, T/4, T/2 and T (T is period)

i know that w = 10^8 here and that k = w/2Pi

i'm killing myself trying to graph this wave at those points in time. please help!

 

[Gokul43201]

Actually, k = w/c, c = 3 X 10^8.
And w/2Pi =1/T or T = 2Pi/w .

k is a wave-vector or an inverse wavelegth. w is a frequency or inverse time. Their dimensions are completely different.

 

[stawbeegirl]

yes you're right. that's what i have written. k = 1/3 (w/c)

to graph do i just plug in 2Pi/w (or multiple of) for t and 1/3 for k?

 

[Gokul43201]

You have

E = 50 cos (wt - kz), where w = 2Pi/T, k = w/c = 1/3

So E = 50 cos (2Pi*(t/T) - z/3)

You are given different values for t/T, ie. 0, 1/4, 1/2, 1. If you plug these in you get E vs. z