Frequency and other properties from E-field

[Breedlove]

Homework Statement

A plane, harmonic, linearly polarized light wave has an electric field intensity given by
{E}_z = {E}_0 cos pi*10^{15}*(t - x/.65c)

while traveling in a piece of glass. Find
(a) The frequency of the light.
(b) Its wavelength.
(c) The index of refraction of the glass.

The Attempt at a Solution

I'm still confused about the argument of the cosine, but I assume that what was within the parenthesis was the real argument. Under this assumption, it fits the form (kx-wt) with some tweaking. The angular frequency w will give me the frequency. I'm pretty sure I need the velocity in order to get the wavelength, and am unsure as to how to find it. Once I get the velocity it will be easy to find the index of refraction.

The problems I ran into:
w=-1 in this case, and so 1/2pi gives me the frequency.
finding velocity of the wave: I used w^{2}/k^{2} = v, however this gives me a value much larger than the speed of light.

Should I just distribute the stuff before the argument? I've never seen a cosine like that. I think that it would be better if it was cos(pi*10^15*(t-x/.65c)) and am confused as to why they didn't do that if that is really what they meant.

Thanks for any help you can provide!

 

[nasu]

Is there a 2 in front of th e"pi" in the formula?

The wave is in the form
E_z=E_0 cos(\omega t -kx) =E_0 cos(2\pi f t -\frac{2\pi}{\lambda}x) =
=E_0 \cos2\pi f ( t -\frac{x}{v})
where I used
\omega=2\pi f, k=\frac{2\pi}{\lambda}, \lambda=c/f
So v=0.6 c, f=10^15 Hz

 

[Breedlove]

Is there a 2 in front of th e"pi" in the formula?

Nope, it's just pi. Thank you so much! I didn't know what k equaled. Thanksthanksthanks.

 

[nasu]

Then 2f =10^15.

 

[berkeman]

Is there a 2 in front of th e"pi" in the formula?

The wave is in the form
E_z=E_0 cos(\omega t -kx) =E_0 cos(2\pi f t -\frac{2\pi}{\lambda}x) =
=E_0 \cos2\pi f ( t -\frac{x}{v})
where I used
\omega=2\pi f, k=\frac{2\pi}{\lambda}, \lambda=c/f
So v=0.6 c, f=10^15 Hz

Please do not post solutions to homework questions.

 

[nasu]

Sorry if I posted more that I was supposed to.
I am aware that the forum policy requires that the poster shows some work and ideas.
I considered that in this case he showed some start and he is only confused about the math manipulation of the formula.
I'll be more careful in the future.

 

[jmaurath]

What is K and lambda, can anyone explain please

 

[berkeman]

What is K and lambda, can anyone explain please

k is the wave number, and Lambda is the wavelength. This page on traveling waves should help you out:

http://en.wikipedia.org/wiki/Travelling_wave#Traveling_waves

.