Light as a Model for Fourier Analysis of                Complex Sound Waves                          Heather M. Whitney, P...
The Scenario∗ Physics of Music course (PHYS205)∗ Targeted towards conservatory students (but many  other students, includi...
Major learning objective∗ Students should understand and be able to describe  the principles of  ∗ Pitch ( frequency)  ∗ ...
Objective                                                         To help                                                 ...
Objective                                                         …and this…Image credit: Johan Sundberg, The Acoustics of...
Objective            …and this…
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 w...
Strategy: (1) use examples from light tointroduce students to the function of the             Fourier transform ∗ Prisms ∗...
PrismsImage credit: Flickr user williamcromar
Emission SpectraImage credit: http://www.microscopy.olympus.eu/microscopes/39_9171.htm
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/sim...
Conclusion∗ A course on the physics of music can utilize ways of  knowing about waves from other fields, such as optics, a...
Thank you!  Heather M. Whitney, Ph.D.    Wheaton College (IL)   Heathermwhitney.comheathermwhitney@gmail.com          @hbarw
Light as a Model for Fourier Analysis of Complex Sound Waves
Light as a Model for Fourier Analysis of Complex Sound Waves
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Light as a Model for Fourier Analysis of Complex Sound Waves

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

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Light as a Model for Fourier Analysis of Complex Sound Waves

  1. 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. 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. 3. Major learning objective∗ Students should understand and be able to describe the principles of ∗ Pitch ( frequency) ∗ Loudness ( amplitude) ∗ Timbre ( waveform)
  4. 4. Objective To help students understand this…Image credit: http://method-behind-the-music.com/mechanics/physics
  5. 5. Objective …and this…Image credit: Johan Sundberg, The Acoustics of the Singing Voice
  6. 6. Objective …and this…
  7. 7. without knowing the math behind this…Image credit: http://www.revisemri.com/questions/creating_an_image/fourier_transform
  8. 8. …and hopefully without this misconception. IMAGE CREDIT: HTTP://XKCD.COM/26/
  9. 9. How?∗ Help non-majors understand the Fourier transform process using the analogy of light.
  10. 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 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.
  11. 11. Strategy: (1) use examples from light tointroduce students to the function of the Fourier transform ∗ Prisms ∗ Emission Spectra
  12. 12. PrismsImage credit: Flickr user williamcromar
  13. 13. Emission SpectraImage credit: http://www.microscopy.olympus.eu/microscopes/39_9171.htm
  14. 14. Emission SpectraImage credit: Andrew M. C. Dawes Image credit: Flickr user kudesai1971
  15. 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/
  16. 16. 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.)
  17. 17. Thank you! Heather M. Whitney, Ph.D. Wheaton College (IL) Heathermwhitney.comheathermwhitney@gmail.com @hbarw
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