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Antinode
- point of maximum displacement on a standing wave
- – Found at the center of the string
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First Mode
- Node at each end and antinode in the center
- – Longest standing wave pattern
- – Represents the lowest possible vibration frequency for the string (f0 / 1st Harmonic)
-
half wavelength resonators
- tubes with two open ends
- model for open vocal tract
- λ = 2L.
- has a peak amplitude at one end,a zero crossing in the center and a second peak amplitude at the other end.
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Quarter Wavelength resonantors
- tubes open at only one end.
- has a zero crossing at the closed end and a peak amplitude at the open end.
- λ=4L
- Model for ear canal. can only vibrate at odd harmonics
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Immitance
a general term that describes how well energy flows through a system
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Impedence (Z)
- opposition to energy flow.
- Impedance dictates how much force must be applied to the mass to move it back and forth at a given velocity.
- the higher the impedance (Z) of the system, the larger the force (F) required to achieve a given velocity (v).
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Mass (positive) Reactance (Xm)
- component of impedance due to mass.
- • Mass opposes movement due to inertia
- • Increases with increasing frequency
- • Opposes high frequency oscillations more than low
-
Stiffness (negative) Reactance (Xs):
- component of impedance due to stiffness.
- Stiffness opposes movement due to restoring force that develops when the spring is displaced.
- Decreases with increasing frequency • Inversely proportional to the frequency of
- vibration.
- Opposes low frequency oscillations more than high.
-
Resistance (R)
component of impedance due to friction
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Friction
- opposes movement because the friction between the block and the surface turns some of the energy into heat. • Frequency Independent •
- Determines how long a system will oscillate •
- Dissipates energy in the form of heat
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Mass & Stiffness Reactance
- The mass and stiffness components of impedance (Xm and Xs) are 180° out of phase with each other.
- – And both of them are 90° out of phase with the resistance component of impedance (R)
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frequency where the system moves most easily• Frequency with the lowest possible impedance
- • Frequency at which Xm = Xs, canceling each other out – Therefore, Impedance (Z) = Resistance (R)
- At frequencies higher
- than Rf: Xm > Xs
- At frequencies lower than Rf: Xm < Xs
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