Chapter 13 - Sound 13.1 Sound Waves. The Production of 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 Heather M. Whitney, Ph.D. Wheaton College (IL) Email: [email protected] Twitter: @hbarw Web: heathermwhitney.com
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Transcript of Light as a Model for Fourier Analysis of Complex Sound Waves
Light as a Model for Fourier Analysis of
Complex Sound WavesHeather M. Whitney, Ph.D.
Wheaton College (IL)
Email: [email protected] Twitter: @hbarw Web: heathermwhitney.com
∗ 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.
The Scenario
∗ Students should understand and be able to describe the principles of ∗ Pitch ( frequency)∗ Loudness ( amplitude)∗ Timbre ( waveform)
Major learning objective
Objective
Image credit: http://method-behind-the-music.com/mechanics/physics
To help students understand this…
Objective
Image credit: Johan Sundberg, The Acoustics of the Singing Voice
…and this…
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/
∗ Help non-majors understand the Fourier transform process using the analogy of light.
How?
Any periodic wave can be synthesized by the sum of a fundamental and its harmonics.
Fourier’s Theorem (1822)
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.
∗ Prisms∗ Emission Spectra
Strategy: (1) use examples from light to introduce students to the function of the
Fourier transform
Prisms
Image credit: Flickr user williamcromar
Emission Spectra
Image credit: http://www.microscopy.olympus.eu/microscopes/39_9171.htm
Emission Spectra
Image credit: Andrew M. C. Dawes Image credit: Flickr user kudesai1971
∗ Use the PhET simulation http://phet.colorado.edu/en/simulation/fourier
∗ Activity available online at http://heathermwhitney.com/resources/
Strategy: (2) Follow up by having students construct waves
∗ 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.)
Conclusion
