ACOUSTICS OF PERCUSSION INSTRUMENTS III' VIBRATIONS OF PLATES, CYMBALS, AND GONGS

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ACOUSTICS OF PERCUSSION INSTRUMENTSIII.
VIBRATIONS OF PLATES, CYMBALS, AND GONGS
Thomas Rossing Stanford University
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SPEED OF WAVES IN A THIN PLATE

LONGITUDINAL WAVES IN AN INFINITE PLATE
QUASI-LONGITUDINAL WAVES IN A FINITE PLATE
? is density, ? is Poisson ratio
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BENDING WAVES IN A PLATE
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RECTANGULAR PLATES
THE DISPLACEMENT AMPLITUDE IS GIVEN BY
WHERE LX AND Ly ARE THE PLATE DIMENSIONS, AND m
AND n ARE INTEGERS (BEGINNING WITH ZERO), THE
CORRESPONDING VIBRATION FREQUENCIES ARE
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VIBRATIONAL MODES OF A RECTANGULAR PLATE
SCAN FIG. 3.9 IN FR
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SQUARE PLATE
SCAN FIG 3.33 IN FR
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VIBRATIONAL MODES OF A CIRCULAR PLATE
FREE EDGE
CLAMPED OR SIMPLY SUPPORTED EDGE
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VIBRATIONAL MODES OF CIRCULAR PLATES
FREE EDGE
CLAMPED (OR HINGED) EDGE
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MODES OF A FLAT CIRCULAR PLATE (ILLUSTRATING
CHLADNIS LAW)
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MODES OF A FLAT CIRCULAR PLATE(PLOTTED vs (m
3n)
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TV HOLOGRAPHY SYSTEM
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46-cm CRASH CYMBAL
46-cm FLAT PLATE
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46-cm FLAT CIRCULAR PLATE
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CYMBALS
CYMBALS HAVE HAD BOTH RELIGIOUS AND MILITARY USE
IN A NUMBER OF CULTURES. ORCHESTRAL CYMBALS ARE
OFTEN DESIGNATED AS FRENCH, VIENESE, AND GERMANIC
IN ORDER OF INCREASING THICKNESS THE TURKISH
CYMBALS USED IN ORCHESTRAS AND BANDS ARE SAUCER
SHAPED WITH A SMALL SPHEERICAL DOME IN THE CENTER
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Historic Cymbals

• Ancient Roman Bronze
• Cymbals

Traditional Chinese Cymbals
Handmade Traditional Turkish Cymbal
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(No Transcript)
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SOUND SPECTRA OF A CYMBAL CHANGES WITH TIME
NOTE THE STRONG AFTERSOUND 50 ms AFTER STRIKING
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DECAY TIMES OF INDIVIDUAL NOTES AND OCTAVE BANDS
IN A 40-cm DIAMETER CYMBAL
SCAN FIG 20.5 IN FR
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WAVES TRAVEL OUTWARD FOLLOWING A CYMBAL STRIKE
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THE ROAD TO CHAOS
NONLINEAR EFFECT IN A CRASH CYMBAL DRIVEN _at_ 192
Hz
HARMONICS FOLLOWED BY SUB-HARMONICS, FOLLOWED BY
CHAOTIC BEHAVIOR
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TAM TAMS
SCAN FIG 20.8 IN FR
BUILDUP AND DECAY OF VIBRATION IN DIFFERENT
FREQUENCY BANDS DURING THE VIRST 0.4 s
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GONGS
SCAN FIG, 20.10 IN FR
GONGS OF DIFFERENT SHAPES
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SOUND SPECTRA OF GONGS
TAWA TAWA GONG
LARGE GAMELAN GONG
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BEIJING OPERA GONGS
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MODES OF LARGE GONG(DA LO)
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SPHERICAL CAP SHELL
CALCULATED MOTION CENTER B
VIBRATION FREQUENCY ? (COMPARED TO SMALL
AMPLITUDE FREQUENCY ?O ) FOR DIFFERENT VALUES OF
NORMALIZED SHELL THICKNESS h/H
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CROTALES
SCAN FIG. 20.14 AND TABLE 20.2 IN FR
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FLEXED PLATES THE MUSICAL SAW
SCAN FIGS. 20.15 AND 20.16 IN FR
DISPERSION CURVES GIVING THE RELATION BETWEEN
WAVE NUMBER k AND FREQUENCY ? FOR THE SECOND
SYMMETRICAL MODE ON A LONG STRIP WITH K AS A
PARAMETER
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GLASS HARMONICA
SCAN COVER OF THE PHYSICS TEACHER
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VIBRATIONAL MODES OF A WINEGLASS
SCAN OR FIND PHOTO
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CARIBBEAN STEEL PANNATIONAL INSTRUMENT OF
TRINIDAD AND TOBAGO
NORTHERN ILLINOIS UNIVERSITY STEEL BAND
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CARIBBEAN STEELPANS
TYPICAL PLAYING RANGES
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SOUND SPECTRA AND MODES OF VIBRATION
SCAN FIG. 20.18 AND 20.19
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TENOR STEELPAN BY CLIFFORD ALEXIS
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COUPLING BETWEEN NOTE AREAS
SCAN FIG. 20.20 IN FR
SMALL AMPLITUDE DRIVE AT BOTTOM, INCREASING TO
LARGE AMPLITUDE AT TOP

• 815 Hz
• (b) 1605 Hz
• (c) 1878 Hz

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SOUND RADIATION FIELD

• Sound intensity is the flow of acoustic power
  through a surface
• A sound intensity probe has two accurately-spaced
  microphones to measure pressure and pressure
  gradient
• Active intensity denotes energy flow to the far
  field
• Reactive intensity denotes energy stored in the
  near field

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SOUND FIELD OF A TENOR PAN F3 note area
MAP OF REACTIVE INTENSITY
MAP OF ACTIVE INTENSITY
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THE PANART HANG
Created by Felix Rohner
Sabina Schärer
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• DING side

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GU side
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The HANG 9 notes tuned to a pentatonic scale

• Eight elliptical note areas are arranged on the
  upper (DING) surface of the HANG around a center
  note area. The principal modes of vibration in
  each note area have frequencies in the ratio of
  321 (except in the highest notes).

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Other HANG scales
7. Hitzaz
1. Aeolian
13.Kourd - Atar / Todi
2. Ake Bono
8. Hitzazkiar - Persian
14. Lydian
3. Banshiki - Cho
15. Minor Penta
9. Hungarian Major

4. Bayati
10. Huzam
16. Neveseri
5. Dorian
11. Ionian
17. Niavent - Egyptian
12. Kokin -Choshi
6. Harmonic minor
and many others
http//www.oddmusic.com/gallery/hang/
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MODES OF NOTE AREAS ON THE HANG

G3 note area
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Active intensity in a plane 8 cm above the top
of the HANG
Arrows show direction of intensity magnitude is
indicated by color
First three resonances of D4
First three resonances of E4
First three resonances of A4
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THANK YOU FOR YOUR ATTENTION