In this exercise, we will write a script to create an instrument sound from scratch.

a. Create a vector, t, of time values from 0 to 2 seconds with length 40,000 samples.

b. Convert the frequency of middle C (261.6 Hz) to ω radians per second.

c. Compute a sound sample as cos(ωt) over the range of t in part a.

d. Play that sound at a sample frequency of 20,000 and verify that it sounds "about right."

e. Perform the Fourier transform on the sound vector, establish the correct axis values and prove that the sound is exactly Middle