Find a waves length given the electric field?

In summary, an electromagnetic wave with an electric field given by E=(3.1x10^5 v/m)*khat*Cos[ky-(12.65*10^12 rad/s)t] is a traveling wave with an amplitude that is a function of both position and time. If time is frozen, the amplitude would appear as a cosine curve fixed in space. If a fixed location is chosen, the amplitude at that location will vary according to a cosine function of time, as the wave moves through that location at the speed of light. Choosing a convenient location and determining the equation for the signal at that location may help in solving the problem.
  • #1
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Homework Statement



an electro magnetic wave has an electric field given by E= (3.1x10^5 v/m)*khat*Cos[ky-(12.65*10^12 rad/s)t]

Homework Equations



k = 2pi/(lambda)


The Attempt at a Solution



I do not know what to sub in for y and t or how to set the equation equal to something so i can solve. So I am pretty much stuck.
 
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  • #2
This is a traveling wave so its amplitude is a function of position and time. At any given instant of time (suppose you cold freeze time), then the amplitude would look like a cosine curve fixed in space.

On the other hand, if you choose a fixed location (y) then the amplitude at that location will vary according to a cosine function of time, the wave moving through that location at the speed of light. You can pick ANY location along the line of the wave and this will be true. What do you think might be a convenient location? What's the equation for the signal at that location?
 

1. What is the formula for finding wavelength given the electric field?

The formula for finding wavelength given the electric field is λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency of the wave.

2. How do I determine the speed of light in a given medium?

The speed of light in a given medium can be determined by dividing the speed of light in a vacuum (c) by the refractive index of the medium (n). This can be expressed as v = c/n.

3. Can I use this formula for all types of waves?

Yes, this formula can be used for all types of waves, including electromagnetic waves, sound waves, and water waves.

4. What units should I use for the electric field and frequency in the formula?

The electric field should be measured in volts per meter (V/m) and the frequency should be measured in hertz (Hz).

5. Is there a relationship between wavelength and frequency in electromagnetic waves?

Yes, there is an inverse relationship between wavelength and frequency in electromagnetic waves. As the frequency increases, the wavelength decreases and vice versa.

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