Presentation at AMATYC Cincinnati, November, 2006

The presentation by June and Bob Decker in pdf format can be downloaded or opened here

The presentation in powerpoint format can be downloaded or opened here

Open Source (and free) software

An applet for comparing two sine functions and their sum (no sound) can be downloaded or run here. In this applet the functions are “standard” textbook sine functions, c*sin(a*x), and d*sin(b*x), graphed over an interval from -30 to 30. It starts with all parameter values equal to one; change “a” or “b” by a small amount to see beats; change the same parameter by a larger amount (try the slider) to observe the complexity of adding just two sine functions.

An applet for comparing two sine functions and their sum, with sound, can be downloaded or run here. In this applet a factor of 2pi is included in each function, and the sum is displayed on two different scales; once over a 0.02 second interval (the same interval as the individual sine functions), and again over a 0.5 second interval (so as to better observe the development of beats). The applet opens with a 440 A and a 660 E (and hence a fifth). Try playing first one, then the other, to hear a fifth. Then play them together. Also try moving one tone close to the other and observe and hear the beats.

A free program for recording and editing sounds, called Wavesurfer, can be downloaded or run here. Use the red button to record a sound, then save as a .wav file. The .wav file can then be converted into data values in a text file (save using a .txt extension), for use in a spreadsheet program, using the applet here.

Excel spreadsheet for Fourier decomposition

An Excel spreadsheet for decomposing a sound into it's component sine functions (a using Excel's built-in Fast Fourier Transform) can be downloaded or run here. Use the programs in the preceding paragraph to record a sound as a .wav file and then convert it to a .txt file, which can be copied into or opened with Excel.