Problem X9
This is a follow-up from Problem A48ab. Here is a chance to see how a wave moves. The electric field of a traveling wave is represented by \(\vec{E}(x,t) = (6\times 10^4)\, \cos(0.5\times 10^7\, x - 1.5\times 10^{15}\, t)\, \hat{k}\), with \(E\) in N/C, \(x\) in meters and \(t\) in seconds.- Use Wolfram Alpha (www.wolframalpha.com) to make a plot of \(E_z\) at both \(t = 0\) and \(t = 10^{-15}\,\text{s}\). Click here to get to Wolfram Alpha with the plot command already entered for \(t=0\). Print these plots (or draw careful sketches of what you see in Wolfram Alpha and attach the plots to your hand-in submission). Is the propagation direction the same as what you determined in Problem A48c? Explain how you know.
- Use the two graphs to determine the speed at which the wave propagates. Compare your answer with what you get from \(\omega/k\).
- Determine the equation for the traveling wave if the wave has a wavelength twice as long as the one that you have been plotting. Make sure that your equation still corresponds to a wave propagating at the speed of light in a vacuum! (Hint: it isn't only the wavenumber that has to be changed.)