3. Here we consider the interference between two harmonic waves at t = 0 (x, t = 0) = cos(k1x) + cos(k2x), (1) with k1 > k2 the propagation numbers of the two harmonic waves. (a) Using a trig identity or, alternatively, complex-representation technique, show that (x, t = 0) = 2 cos(K+x) cos(Kx), (2) with K = (k1 k2)/2 > 0. The interference of these two waves can therefore be expressed as a product cosine functions with different propagation numbers K. (2pts) (b) Construct a Matlab code to plot the initial wave (x, t = 0) according to both Eqs. (1) and (2) on the interval x = [0, 120] for k1 = , k2 = 0.95, and provide plots of your output verifying that the plots agree. You should see the spatial interference fringes we talked about in class, with a fast carrier wave that is modulated by a slower envelope. Identify which of the factors in the above expressions corresponds to the envelope. Please submit a listing of your code with your numerical plot(s).

the interference between two harmonic waves at (x,t = 0) = cos( z) + cos(k22), with ki > k2 the propagation numbers of the two harmonic waves. (a) Using a trig identity or, alternatively, complex-representation technique, show that (,t-0)-2 cos(K+ cos(Ka) with K = (kit k2)/2 > 0, The interference of these two waves can therefore be expressed as a product cosine functions with different propagation numbers Kt. (2pts) (b) Construct a Matlab code to plot the initial wave (z, t 0) according to both Eqs. (1) and (2) on the interval z = 0. 120 for k-T,k2 = 0.95m and provide plots of your output verifying that the plots agree. You should see the spatial interference fringes we talked about in class, with a fast carrier wave to the envelope. Please submit a listing of your code with your numerical plot(s). (3pts) PART B PLEASE. I need the MATLAB code the interference between two harmonic waves at (x,t = 0) = cos( z) + cos(k22), with ki > k2 the propagation numbers of the two harmonic waves. (a) Using a trig identity or, alternatively, complex-representation technique, show that (,t-0)-2 cos(K+ cos(Ka) with K = (kit k2)/2 > 0, The interference of these two waves can therefore be expressed as a product cosine functions with different propagation numbers Kt. (2pts) (b) Construct a Matlab code to plot the initial wave (z, t 0) according to both Eqs. (1) and (2) on the interval z = 0. 120 for k-T,k2 = 0.95m and provide plots of your output verifying that the plots agree. You should see the spatial interference fringes we talked about in class, with a fast carrier wave to the envelope. Please submit a listing of your code with your numerical plot(s). (3pts) PART B PLEASE. I need the MATLAB code