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 velocitypoint of minimum pressurehigh kinetic energyconstriction at this point will lower the resonant frequencyVelocity node - pressure antinode (P)point of minimum velocitypoint of maximum pressurehigh potential energyconstriction at this point will raise the resonant frequencyQuestions 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 = (2n-1)c = 3*35,000 = 1640 Hz4L 4*16Use 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?2) Do you expect F2 to be higher or lower than 1640 Hz if the vocal tract is constricted in the pharynx?3) Do you expect F2 to be higher or lower than 1640 Hz in the vowel [i]?4) Approximately what is the frequency of F2 in [u], assuming that the VT length is 16 cm?1Standing wave of F2 with velocity nodes and antinodes labeled - waveform represents pressure profile of standing wave. Standing wave of F2 with velocity nodes and antinodes labeled - waveform represents velocity profile of standing wave.Answers:1) Do you expect F2 to be higher or lower than 1640 Hz if the vocal tract is constricted at the lips? - lower, because constriction at a velocity antinode (V in the figure) will lower the resonant frequency.3) Do you expect F2 to be higher or lower than 1640 Hz in the vowel [i]? - higher, because [i] has a constriction near the hard palate and this is at a velocity node (P in the figure) and constriction at a velocity node will increase the resonant frequency.4) What is the frequency of F2 in [u]? lower than 1640Hz, probably much lower, because two velocity antinodes, one at the lips and one at the back of the tongue, are constricted in
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