lecture19

# lecture19 - String Instruments 1 General comments Vibration...

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String Instruments 1. General comments Vibration of strings - standing waves Fundamental: Harmonics: The fundamental frequency and harmonics are determent by length, L , tension, F, and linear mass density, μ. Usually, length and mass of the string remain constant, and turning is accomplished by changing tension. Timbre is mainly determined by harmonics The combination of harmonics depends on the method of string excitation (plucked, bowed or struck by a hammer; exited in the center or at the edge), and on the resonances (ear and wood resonances) ( 29 L v v f L 2 ; 2 / 1 1 = = = λ λ 1 1 ; / nf f n n n = = λ λ μ F v =

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2. Vibration of a plucked string http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html Some properties: String plucked at its center contains only odd harmonics. Intensity of these harmonics decays as 1/n 2 , where n is the harmonic’s number If distance from the end is 1/n (n=1,2,3…) then n-th harmonic is missing Harmonic Ampliude Phase 1 1 + 2 0 none 3 1/9 - 4 0 none 5 1/25 + 6 0 none 7 1/49 - Plucked at its center Harmonic Ampliude Phase 1 1 + 2 0.40 + 3 0.18 + 4 0.06 + 5 0 none 6 0.03 - Plucked at 1/5 of length
3. Vibration of a bowed string Displacement and velocity During the grater part of each period, the string is carried along by bow. Then it suddenly detaches itself and moves rapidly beck until it is caught by the moving bow again. Frequency is determent by length, L , tension, F, and linear mass density, μ. The beginning and the end of slippage depend on position of the bow. For each position there is maximum and minimum bowing force. Closer to the bridge these forces are stronger.

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4. Violin Violin Construction: four strings (of steel or gut) tuned to G 3 , D 4 , A 4 , E 5 (196.0, 293.7, 440.0, 659.3 Hz) What is the interval?
Vibration of the violin body. Important factor in sound quality To determine normal modes forces can be applied to the bridge Most of the sound that a listener hears from a violin is radiated into the air from the top and back plates The sound quality can be changed considerably by the place where the string is bowed:

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