Sine Waves and Sound David R. Hill & Lila F. Roberts Used with permission all rights reserved.

OUTLINE Report: A work in progress. Beta version is available at Demo Objective: To develop the connection between sine waves and the sounds that they can generate. (Tones) Level: This demo can be used at the precalculus or calculus level. It may also be used in introductory courses on speech and hearing. Technology Involved: Basic knowledge of Excel if the included interactive Excel worksheet is used. Also included is MATLAB support and suggested experiments. Demo the Excel worksheet. (Hopefully) Can be used for in-class demos or student assignments.

Background: It’s all her fault!

Is It Live or is it Memorex®? Memorex debuted in the 1970s with the introduction of its Recordable Audio Cassette, and legendary jazz virtuoso Ella Fitzgerald demonstrating the tagline "Is it live, or is it Memorex?" Memorex will send a video tape upon request.

In the DEMOS with POSITIVE IMPACT collection is demo Using Sound to "Illustrate" Mechanical Vibrations The tool used is MATLAB. This is appropriate for a differential equations class.

For CALCULUS, I show sine wave animations to illustrate amplitude, period, and phase shift. These are available at When used with QuickTime you can stop/start/talk/explain, etc.

I also use an Excel tool with sliders to vary the amplitude, period, and phase shift.

Incorporate sound for sine waves. To do that we should change things to acoustic format, which is what is used in signal processing and speech and hearing classes. So now we get to modify the standard math format. We need frequency f and Hertz, the unit of frequency which is cycles per second. So we get an equation change: Now we can change the Excel demo file!

 = ( 

Incorporating Sound Just simple tones to illustrate amplitude and frequency. HELP! Why not search the web!!! Diane Kewley-Port, Professor of Speech and Hearing Sciences at Indiana University to the rescue. She has a student project that is part of the course Mathematical Foundations of Speech and Hearing which involved WaveWriter macro. (We have permission to use this macro.) demo

SONIFICATION: the use of non-speech audio to convey information. “Integrating Sonification into Calculus Instruction”, Steve Hetzler/Bob Tardiff, Math/Computer Science, at Salisbury University, NSF “Sonfication as Mathematics Teaching Tool”, proceedings/papers/upson.pdf A search on sonification finds other interesting information. Software: Goldwave a digital audio editor.

SUMMARY To complement visualization tools for sine waves; tone sounds can be created for in-class use or for a student assignment. The Excel demo files can be easily modified for local use. In the Demos with Positive Impact collection there is a freely available demo that contains both the visualization and sound generation tools discussed. Go to This is a beta version. Comments/suggestions are welcome. A large collection of other (free) demos is available at THANKS!