2. Complex Vibrations - Exercises

Instructions:  Complete the following exercises, using the functions defined in the tutorial.

1. Type your name here:

2. When you are finished, remove any graphs or sounds that you produced, BUT LEAVE THE INSTRUCTIONS THAT PRODUCED THESE GRAPHS OR SOUNDS.  (Please remove the graphs and/or sounds that came with the notebook as well.)  Also, leave your typed answers to the questions posed.

Exercise 1:  Creating a periodic waveform

(a)   Use the base frequency for the musical note C4 (261.1 Hz) and create a graph of this waveform for several periods of oscillation.  What is the period, in ms, of this waveform?

(b)  Add another waveform, with a frequency that is 3/2 as much as the frequency used in part (a),  but with the same amplitude, to the waveform you created in part (a).  What is the period of oscillation of the new component alone?  What is the period of oscillation of the combined waveform?

(c) Take the complex waveform you created in part (b) and use the Mathematica Play function to listen to the sound of this waveform for a second or so.    How does it sound?  i.e.  does it seem to be consonant or dissonant?

2: NonPeriodic WaveForms

Exercise 2:  Creating a non-periodic waveform

(a)  Start with the C4 waveform as in Exercise 1 and add another waveform to it, except this time add a frequency that is (Sqrt[2]) as big as the frequency used in part (a),   with the same amplitude.  Plot the graph of the complex waveform for at least 10 periods of the C4.  From the graph, can you discern the period of oscillation of the combined waveform?

(b) Take the complex waveform you created in part (a) and use the Mathematica Play function to listen to the sound of this waveform for a second or so.    How does it sound?  i.e.  does it seem to be consonant or dissonant?