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PH 105

PH 105. Dr. Cecilia Vogel Lecture 19. OUTLINE. PERCUSSION Membrane vibrations Labeling convention plates bells bars Indefinite pitch. Membrane Modes. A membrane is like a string, but 2-D To vibrate it must be stretched.

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PH 105

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  1. PH 105 Dr. Cecilia Vogel Lecture 19

  2. OUTLINE • PERCUSSION • Membrane vibrations • Labeling convention • plates • bells • bars • Indefinite pitch

  3. Membrane Modes • A membrane is like a string, but 2-D • To vibrate it must be stretched. • A membrane clamped around the edge has a node all along edge. • In lowest mode, this is the only node • In higher modes, also have additional nodes • Radial nodes • Circular nodes

  4. Notation • The membrane may have • Radial nodes • go across the membrane • Circular nodes • go around the membrane • Modes are labeled by • # of radial nodes • then # of circular nodes 02 mode 11 mode 32 mode

  5. Membrane Frequency • The resonant frequencies of vibration of membrane • Decreases as radius increases, • Increases as tension increases, • Decreases as density increases.

  6. Overtones • The overtones of a membrane are not harmonic. (Fig 13.9) • If you strike membrane at center • Excite 01, 02, 03, …, vibrate at center • Not harmonic, dies off quickly. • If you strike membrane in usual way, • Excite 11, 21, 31, …, not vibrate at center • Consonant: (Fig 13.9)2.14/1.59 ≈ 4/3 (about fourth), 2.65/1.59 = 5/3 (major sixth) • Ring

  7. Cymbals • Cymbals are similar to membranes, except • Stiff — higher freq • Not clamped at edges, so • It has modes with zero circular nodes • Modes similar to circular plates in lab.

  8. Carillon Bells • Bells are very similar to plates • that have been bent down at the edges. • Modes Fig 13.30 • video animation of modes

  9. Bar Vibrations • Bars are like strings, except • stiff • not clamped at the ends • Fig 2.17 modes of uniform bar • relate to lab observations • note non-harmonic • Gamut bells • overtones die quickly • pure tone quality from ringing fundamental • VIDEO

  10. Non-uniform Bars • Uniform bars have inharmonic overtones • Can shape bar, give it an arch • to tune the overtones to be more harmonic • Marimba bars freq’s in Fig 13.1 • find ratio f/f1 2 octaves 4 octaves 4 octaves + fifth (16)(3/2)

  11. Indefinite Pitch • Many percussion instruments • have indefinite pitch. • There is no strong, ringing fundamental. • There is no harmonic structure • because of inharmonic overtones. • Fig 13.7, 13.12. • bass drum, snare drum, triangles

  12. Summary • Modes of bars • determined by # nodes, like string. • Modes of plates and membranes • have radial and circular nodes • Resonant freq’s of percussion instruments often not harmonic • sometimes pitch is determined by strong fundamental • sometimes overtones are tuned to consonant intervals • sometimes no definite pitch

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