Title: 2nd Step: Using Math to Represent a Sound Wave
Course: Sound Physics

By this time you should understand that simple sound waves are really just variations of air pressure with time that repeat themselves over and over.  The loudness or intensity is related to the strength of the air pressure difference compared to the normal air pressure and the pitch is related to how frequently the wave is made with time.  A math funtion which can represent this same thing is the Sine Wave Curve.  It has amplitude and it repeats itself so we will practice graphing some different waves so you can see how it works.

1. Open this website Function Grapher in a new window.
2. Graphing is really easy.  As an example you can graph both the function y=x and the function y=2x on the same graph simply by typing   x;2x   in the text window as shown here.
3. A simple sound wave graph can be modeled by using the sin function in this form y=Asin(2*pi*f*x) where y could stand for the pressure, A the amplitude, pi is 3.14, f is the frequency and x would be the time.
4. To graph a 440 hz wave sound wave just type 5sin(2pi440x) into the text window and take a look at the graph of this simple wave.
5. Sound Waves are usually made up of more than one frequency.  When real instruments play notes they are usually made up of more than one frequency of varying amplitudes.  This gives the instrument its characteristic sound or Timbre.  Try adding more than one frequency such as a 440 Hz and maybe half the amplitude 480 Hz and see what happens in the grapher. Create your own interesting sound in audacity or with an instrument and model it with sin waves n the function grapher.  Upload a image of your audacity file and your function grapher file here to compete Assignment 4.