Music as Math Waves: Exploring Trigonometry Through Sound

Candace M. Quinn, Middle Tennessee State University
Derek K. Smith, Nashville State Community College
Michaele F. Chappell, Middle Tennessee State University
Susan D. Carver, Cleveland State University
Stephen F. Duffy PhD, PE, Cleveland State University
John P. Holcomb Jr., Cleveland State University
Debbie Jackson, Cleveland State University
Andrew Resnick, Cleveland State University

This material is based upon work supported by the National Science Foundation under Grants No. DUE-1161152 and HRD-1304371. Cleveland State University also contributed substantially to this effort.


Students studying transformations of trigonometric functions may learn formulas associated with period and frequency without developing an understanding of the concepts themselves. In this article, the authors present a task that uses arts integration in the form of sound waves to help students explore the relationship between period and frequency. Students are guided through a task of generating a ringtone for a smartphone that blends music, maths, and technology. Links to worksheets and a sample ringtone are provided to facilitate a teacher's implementation of the task; suggestions and advice are included. Using the arts to teach traditional STEM topics, an initiative known as STEAM offers promising opportunities for students to apply creative elements to solve technical problems. Although the topic in this article is suitable for precalculus students, STEAM-based instruction is applicable across multiple grade levels.