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The Science of Sound Dr. Bill Pezzaglia, CSUEB Physics

Delve into the physics of percussive instruments like bars, rods, plates, and drums. Learn about vibration modes, Chladni patterns, and tuning forks, unraveling the mysteries of sound production. Updated with fascinating insights as of 2012.

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The Science of Sound Dr. Bill Pezzaglia, CSUEB Physics

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  1. 1 The Science of SoundDr. Bill Pezzaglia, CSUEB Physics Category: Musical Instruments Topic: Percussive Instruments Updated 2012May15

  2. 2 Percussive Instruments • Bars and Rods • Plates • Membranes (drums) • References

  3. 3 A. Bars & Rods • Bending Beam • Tuning Fork • Xylophone Demo: http://www.falstad.com/barwaves/

  4. 4 a. Clamped End Beam Typically used in a music box

  5. 5 a. Clamped Bar Modes “L” is length of square bar “a” is thickness of bar “c” is the speed of sound in the bar “x” is one of solutions to cos(x)cosh(x)=-1 (1.8751, 4.694, 7.855 …) Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c2

  6. 6 b. Tuning Fork • Invented in 1711 (1712?) by British musician John Shore (Handel’s trumpeter?) • Used to give a pure tone for tuning instruments • Used in Accutron watches!

  7. 7 b. Tuning Fork Modes Tuning fork is like two clamped bars. By symmetry, only the odd harmonics are present. The 3rd drops out quickly. Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/tunfor.html#c1

  8. 8 c. Xylophone A beam free at both ends. Supports make it play the fundamental mode. Reference: http://www.kettering.edu/~drussell/Demos/Flexural/bending.html

  9. 9 c. Free bar modes At the moment, I’m not at all sure where these numbers come from. Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c3

  10. 10 Approximate Formulas Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c2

  11. 11 B. Plates • Chladni • Rectangular Plate • Circular Plate

  12. 12 1. Ernst Chladni (1756—1827) • First measurement of speed of sound in solids (up to 40x faster than in air!) • Measures speed of sound in different gases(slower in heavier gases) • 1787 “Chladni Plate” shows vibration of sound using sand on a plate.

  13. 13 Chladni’s drawings of patterns 1808 Chladni’s demonstration at the French Academy of Science led to the Emperor promising 1 kilogram of gold to the first person who could give a theory to explain the phenomena.

  14. 14 More Patterns (John Tyndall 1869)

  15. 15 Chladni Square Plate Formula Line of nodes are solutions to: Frequency:

  16. 16 2. Vibration of Rectangular Plate Two dimensional vibration “nodes” (places of no displacement) are now lines

  17. 17 Demo link • http://people.uncw.edu/hermanr/pde2/Membranes/Rectangular/index.htm

  18. 18 3. Chladni Circular Plate Ref: http://www.nhn.ou.edu/~johnson/Education/Juniorlab/Chladni/2001-ChladniPlates-CurtisParry.pdf

  19. 19 3. Circular Plate “Nodes” are radial lines and circles

  20. 20 C. Membranes (Drums) Demos: http://www.falstad.com/membrane/ http://www.falstad.com/circosc/index.html Demo: http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html

  21. 21 References • http://www.santafevisions.com/csf/html/lectures/016_instruments_III.htm

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