Part III: Sine Waves Sine waves can be represented by the following equation: y(t) = A * sin (til) where A is the amplitude, is the frequency and is the phase. a. Plot a simple sine wave with amplitude and frequency equal to one and phase equal to zero. To do this you have to create two matrices, lets call them sa and t. First, create the t matrix from time 0 to 10 seconds. Make the increments.01 seconds. Now, create the matrix s using the following command: sa = sin(t). Next, plot this sine wave. b. Now, let us change one parameter at a time for the sine wave. Create a new sine wave with an amplitude of your choice. Leave the frequency at one and the phase at zero. Name the matrix sb. You can use the same time matrix, t, created in step a. Next, plot this sine wave. c. Now do the same as in step b_hut change the frequency to a value of your choice. Leave the amplitude at one and the phase at zero. Name the matrix se. d. Now do the same as in step b, but for the phase. Leave the Amplitude and frequency at one. Name the matrix sd. e. Now plot all the waves in one graph. You can do this using this command: plot(t.saj.sh.sc.Jesd) f. In the graph window, select Insert Legend. This will allow you to distinguish which graph corresponds to which data. So datal is the sa wave, data2 is the sb wave and so on. g. Now, create a new wave, call it super Waxe, that is composed of the four waves created in the perxious, steps. You can do this by: superWaxe = sa + sb + s + sd Plot superWave using the same time matrix, t. h. Observing the graph of superWave, how difficult, do you think, is it for a human to determine the original sine waves that created superWaxe? In the next part of the lab, we will investigate a technique that gives us the simple sine waves that make up more complex waves