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Antinode
 point of maximum displacement on a standing wave
 – Found at the center of the string

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.

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

Immitance
a general term that describes how well energy flows through a system

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).

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

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

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)

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

