Find a waves length given the electric field?

AI Thread Summary
To find the wavelength of the electromagnetic wave described by the electric field E = (3.1x10^5 V/m) k-hat Cos[ky - (12.65x10^12 rad/s)t], the wave number k can be used, where k = 2π/λ. The challenge lies in determining appropriate values for y and t to analyze the wave's behavior. At a fixed location, the amplitude varies over time according to a cosine function, while at a fixed time, the amplitude appears as a stationary cosine curve. A convenient approach is to select a specific location along the wave and derive the equation for the signal at that point. Understanding these relationships is crucial for solving for the wavelength.
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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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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?
 
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