Perturbation theory.
Aim of the theory
 predict the frequencies of formants relative to resonances of a uniform tube, based
on how changes in tube geometry impact standing waves.
Velocity antinode  pressure node (V)
point of maximum velocity
point of minimum pressure
high kinetic energy
constriction at this point will lower the resonant frequency
Velocity node  pressure antinode (P)
point of minimum velocity
point of maximum pressure
high potential energy
constriction at this point will raise the resonant frequency
Questions about F2.
Suppose that the vocal tract is 16 cm long.
Calculate the frequency of F2 for the uniform tube open at
one end and closed at the other  no constrictions in the vocal tract like [schwa].
F2 = (2n1)c
=
3*35,000
=
1640 Hz
4L
4*16
Use the graphs of the F2 standing wave (over) to answer these questions:
1) Do you expect F2 to be higher or lower than 1640 Hz if the vocal tract is constricted at the lips?
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 Fall '08
 kjohnson
 Ode, Wavelength, vocal tract, Standing wave, resonant frequency

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