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The Science of Sound Dr. Bill Pezzaglia, CSUEB Physics

1. The Science of Sound Dr. Bill Pezzaglia, CSUEB Physics. Category: Musical Instruments Topic: Percussive Instruments Updated 2012May15. 2. Percussive Instruments. Bars and Rods Plates Membranes (drums) References. 3. A. Bars & Rods. Bending Beam Tuning Fork Xylophone.

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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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