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Physics 1251 The Science and Technology of Musical SoundPhysics 1251 Unit 3 Session 34 Percussion with PitchSlide 3Slide 4Slide 5Physics 1251 Unit 3 Session 33 PercussionSlide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Physics 1251Physics 1251The Science and The Science and Technology of Musical Technology of Musical SoundSoundPhysics 1251Physics 1251The Science and The Science and Technology of Musical Technology of Musical SoundSoundUnit 3Unit 3Session 34 MWFSession 34 MWFPercussion with PitchPercussion with PitchUnit 3Unit 3Session 34 MWFSession 34 MWFPercussion with PitchPercussion with PitchPhysics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with PitchA percussionist has two nearly A percussionist has two nearly identical cymbals. They have identical cymbals. They have identical fundamental frequencies, identical fundamental frequencies, but one is 15 inches in diameter but one is 15 inches in diameter while the other is 14 inches in while the other is 14 inches in diameter. What must be true diameter. What must be true about the two?about the two?The larger cymbal must be about The larger cymbal must be about 15% thicker than the smaller one, 15% thicker than the smaller one, since the frequency is proportional to since the frequency is proportional to the thickness and inversely the thickness and inversely proportional to the square of the proportional to the square of the diameter.diameter.Physics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with Pitch11′ Lecture:′ Lecture:•Piano strings exhibit inharmonicity because Piano strings exhibit inharmonicity because of the stiffness of the wire.of the stiffness of the wire.•Some percussion instruments have pitch. Some percussion instruments have pitch. •Pitch results from a harmonic series of Pitch results from a harmonic series of overtones.overtones.•Tympani and Tabla are pitched drums.Tympani and Tabla are pitched drums.•Orchestra Chimes, Glockenspiel, Orchestra Chimes, Glockenspiel, Xylophone, Marimba and Vibraphone have Xylophone, Marimba and Vibraphone have intonation.intonation.Physics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with PitchThe Percussion InstrumentsThe Percussion InstrumentsPercussion – strikingPercussion – strikingPianoPianoHammer Hammer dulcimerdulcimerCymbals, Gongs, Cymbals, Gongs, PansPansXylophones, chimesXylophones, chimesOthersOthersDrumsDrumsMembranesMembranesBlocks, Blocks, bells, bells, shellsshellsPlatesPlatesBarsBarsStringsStringsPhysics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with Pitch80/2080/20The task of producing pitch in a The task of producing pitch in a percussion instrument is an percussion instrument is an exercise in manipulating the exercise in manipulating the overtones into a harmonic series.overtones into a harmonic series.FrequencyFrequencyAmplitudeAmplitudeff0011ffn mn m = = xxn mn m ff1010 UnpitchedUnpitchedAmplitudeAmplitudeff112f2f113f3f114f4f11ffnn = n f = n f11 PitchedPitchedPhysics 1251Physics 1251Unit 3 Session 33Unit 3 Session 33 PercussionPercussionThe Modes of vibration of an ideal The Modes of vibration of an ideal string are harmonic. string are harmonic. • • Linear Linear density density μμ= = mass/lengthmass/length• • Tension Tension TT= force= forceffn n = n /( = n /(2 L) 2 L) ‧ √(T/ ‧ √(T/ μ) μ) nn = 1, 2, 3, 4, 5, = 1, 2, 3, 4, 5, 6, 7….6, 7….Tension TTension TLinear density Linear density μμLLThe stiffness of the The stiffness of the wire increases the wire increases the frequency of the frequency of the higher frequency higher frequency harmonics.harmonics.₧ ₧ = 3986= 3986¢ Log(nf¢ Log(nf1 1 /440) /440) + + II((₧) ₧) II((₧) = Inharmonicity₧) = InharmonicityPhysics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with PitchInharmonicity of PianoInharmonicity of PianoPitch Pitch ((¢)¢)InharmoniInharmonicitycityBecause of the inharmonicity of strings Because of the inharmonicity of strings the octaves are “stretched” in a piano.the octaves are “stretched” in a piano.2020¢¢4040¢¢-20-20¢¢Physics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with PitchTympani and TablaTympani and TablaPhysics 1251Physics 1251Unit 3 Session 33Unit 3 Session 33 PercussionPercussionOrchestral PercussionOrchestral PercussionTympaniTympaniPhysics 1251Physics 1251Unit 3 Session 33Unit 3 Session 33 PercussionPercussionTympani are tuned by adjusting Tympani are tuned by adjusting the tension on the the tension on the head.head.Tension Tension devicedeviceTension Tension pedalpedalPhysics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with PitchThe Modes of Oscillation The Modes of Oscillation of an (Ideal) of an (Ideal) Clamped MembraneClamped MembraneMode: Mode: (0,1)(0,1)ff0 10 1 = 0.7655/ = 0.7655/ d d ‧ √(S/ ‧ √(S/ σ)σ)Mode: Mode: (1,1)(1,1)ff1 11 1 = 1.594 f = 1.594 f0 10 1 Mode: Mode: (2,1)(2,1)ff2 12 1 = 2.136 f = 2.136 f0 10 1 Surface Surface Tension STension SSurface density Surface density σσPhysics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with PitchAir Loading of a Clamped Air Loading of a Clamped MembraneMembraneSurface Surface Tension STension SSurface density Surface density σσAir Air massmassThe mass of air The mass of air moved by the moved by the membrane adds to membrane adds to the effective surface the effective surface density, lowering the density, lowering the frequency.frequency.Physics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with Pitch80/2080/20The kettle of Tympani modifies the The kettle of Tympani modifies the membrane frequencies by the membrane frequencies by the interaction of the air resonances interaction of the air resonances with the surface modes.with the surface modes.Modes of air vibrationModes of air vibrationPhysics 1251Physics 1251Unit 3 Session 34Unit 3 Session 34 Percussion with PitchPercussion with PitchThe Modes of Oscillation The Modes of Oscillation of of


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