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

2. Percussive Instruments A.Bars and Rods B.Plates C.Membranes (drums) D.References 2

3. A. Bars & Rods 1.Bending Beam 2.Tuning Fork 3.Xylophone 3 Demo: http://www.falstad.com/barwaves/http://www.falstad.com/barwaves/

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

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 …) 5 Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c2

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! 6

7. b. Tuning Fork Modes Tuning fork is like two clamped bars. By symmetry, only the odd harmonics are present. The 3 rd drops out quickly. 7 Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/tunfor.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/music/tunfor.html#c1

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

9. c. Free bar modes At the moment, I’m not at all sure where these numbers come from. 9 Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c3

10. Approximate Formulas 10 Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/music/barres.html#c2

11. B. Plates 1.Chladni 2.Rectangular Plate 3.Circular Plate 11

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. 12

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. 13

14. More Patterns (John Tyndall 1869) 14

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

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

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

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

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

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

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