How Do You Find the Frequency of a 550 nm Harmonic Wave in Vacuum?

[anubis01]

Homework Statement

A 550 nm harmonic wave whose electric field is in the z direction is traveling in the y direction in vacuum.

a)find the frequency of the wave
b)determine $$\omega$$ and k.
c)if the electric field amplitude is 600 V/m find the amplitude of the magnetic field.
d)write an expression for both E(t) and B(t) given that each is zero at x=0 and t=0.

Homework Equations

$$\Psi$$(x,t)=Acos(kx-$$\omega$$t)+Csin(kx-$$\omega$$t)

The Attempt at a Solution

I've solved all the other questions but part d is giving me a bit of trouble.

$$\Psi$$(x,t)=Acos(kx-$$\omega$$t)+Csin(kx-$$\omega$$t)
$$\Psi$$(0,0)=Acos(0) + Csin(0)
0=A(1) + C(0)
therefore A=0 but not necessarily C so i wrote
E(t)=$$\hat{y}$$Csin(kx-$$\omega$$t) and
B(t)=$$\hat{z}$$Csin(kx-$$\omega$$t)

This is the part I'm stuck on, I'm unsure on how to solve for the constant C, the amplitude of the function.

*edit the formatting is a bit off, it should be kx-wt, the w isn't a power of anything.

 

[gabbagabbahey]

First, $\textbf{E}(\textbf{r},t)=C_E\sin(kx-\omega t)\mathbf{\hat{y}}$ describes an electric field, with amplitude $C_E$, polarized in the $y$-direction, and traveling in the $x$-direction...that isn't what the problem statement you've posted asks you to describe...

 

[anubis01]

Thank you for the quick reply. Since my idea is wrong, could you give me a hint on the correct way to solve the problem.

 

[gabbagabbahey]

Remember, the general form of a plane wave, traveling along the direction of $\mathbf{k}$ and polarized in the $\mathbf{\hat{n}}$ direction is [itex]\textbf{E}(\textbf{r},t)=C\sin(\mathbf{k}\cdot\textbf{r}-\omega t)\mathbf{\hat{n}}+D\cos(\mathbf{k}\cdot\textbf{r}-\omega t)\mathbf{\hat{n}}[/tex]

What would you expect $\mathbf{\hat{n}}$ to be if the field is polarized in the $z$-direction?

What would you expect $\mathbf{k}\cdot\textbf{r}$ to be if the field is traveling in the $y$-direction?