An invited talk by Heather M. Whitney at AAPT Winter 2013.

1. Light as a Model for Fourier Analysis of
Complex Sound Waves
Heather M. Whitney, Ph.D.
Wheaton College (IL)
Email: heathermwhitney@gmail.com Twitter: @hbarw Web: heathermwhitney.com

2. 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.

3. Major learning objective
∗ Students should understand and be able to describe
the principles of
∗ Pitch ( frequency)
∗ Loudness ( amplitude)
∗ Timbre ( waveform)

4. Objective
To help
students
understand
this…
Image credit: http://method-behind-the-music.com/mechanics/physics

5. Objective
…and this…
Image credit: Johan Sundberg, The Acoustics of the Singing Voice

6. Objective
…and this…

7. without knowing the math behind this…
Image credit: http://www.revisemri.com/questions/creating_an_image/fourier_transform

8. …and hopefully without this
misconception.
IMAGE CREDIT:
HTTP://XKCD.COM/26/

9. How?
∗ Help non-majors understand the Fourier transform
process using the analogy of light.

10. 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 unseen
components that can be identified using tools
appropriate to the phenomena. These tools separate
the waves into their components, and their different
amplitudes and frequencies can then be observed.

11. Strategy: (1) use examples from light to
introduce students to the function of the
Fourier transform
∗ Prisms
∗ Emission Spectra

12. Prisms
Image credit: Flickr user williamcromar

13. Emission Spectra
Image credit: http://www.microscopy.olympus.eu/microscopes/39_9171.htm

14. Emission Spectra
Image credit: Andrew M. C. Dawes Image credit: Flickr user kudesai1971

15. 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/

18. 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.)

19. Thank you!
Heather M. Whitney, Ph.D.
Wheaton College (IL)
Heathermwhitney.com
heathermwhitney@gmail.com
@hbarw