Light as a Model for Fourier Analysis of Complex Sound Waves
Light as a Model for Fourier Analysis of Complex Sound Waves Heather M. Whitney, Ph.D. Wheaton College (IL)Email: email@example.com Twitter: @hbarw Web: heathermwhitney.com
The Scenario∗ Physics of Music course (PHYS205)∗ Targeted towards conservatory students (but many other students, including a few physics majors!)∗ Course description: Physics of Music. Basic concepts of sound and acoustics; vibrations, waves, fundamentals and overtones, musical scales, harmony, noise, physical and physiological production, and detection of sound waves; acoustical properties of materials and enclosures.
Major learning objective∗ Students should understand and be able to describe the principles of ∗ Pitch ( frequency) ∗ Loudness ( amplitude) ∗ Timbre ( waveform)
Objective To help students understand this…Image credit: http://method-behind-the-music.com/mechanics/physics
Objective …and this…Image credit: Johan Sundberg, The Acoustics of the Singing Voice
without knowing the math behind this…Image credit: http://www.revisemri.com/questions/creating_an_image/fourier_transform
…and hopefully without this misconception. IMAGE CREDIT: HTTP://XKCD.COM/26/
How?∗ Help non-majors understand the Fourier transform process using the analogy of light.
Fourier’s Theorem (1822) Any periodic wave can be synthesized by the sum of a fundamental and its harmonics.Observed waves can be made up of unseencomponents that can be identified using toolsappropriate to the phenomena. These tools separatethe waves into their components, and their differentamplitudes and frequencies can then be observed.
Strategy: (1) use examples from light tointroduce students to the function of the Fourier transform ∗ Prisms ∗ Emission Spectra
Emission SpectraImage credit: Andrew M. C. Dawes Image credit: Flickr user kudesai1971
Strategy: (2) Follow up by having students construct waves∗ Use the PhET simulation http://phet.colorado.edu/en/simulation/fourier∗ Activity available online at http://heathermwhitney.com/resources/
Conclusion∗ A course on the physics of music can utilize ways of knowing about waves from other fields, such as optics, as well as activities associated with that discipline, to help students better understand the function of the Fourier transform, which contributes to the understanding of waveforms (and timbre.)
Thank you! Heather M. Whitney, Ph.D. Wheaton College (IL) Heathermwhitney.firstname.lastname@example.org @hbarw