The Science of Sound Dr Bill Pezzaglia CSUEB

The Science of Sound Dr. Bill Pezzaglia, CSUEB Physics Category: Musical Instruments Topic: Percussive Instruments Updated 2012 May 15 1

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

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

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

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#c 2 5

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

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. Ref: http: //hyperphysics. phy-astr. gsu. edu/hbase/music/tunfor. html#c 1 7

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 8

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#c 3 9

Approximate Formulas Ref: http: //hyperphysics. phy-astr. gsu. edu/hbase/music/barres. html#c 2 10

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

1. Ernst Chladni (1756— 1827) • First measurement of speed of sound in solids (up to 40 x 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

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

More Patterns (John Tyndall 1869) 14

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

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/pde 2/Membranes/Rectangular/index. htm

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

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

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

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