Perturbation Theory

[Rory F]

Hello,

I’m still getting my head around Perturbation Theory:

“if the vocal tract is constricted at a point of high potential energy (pressure maximum), air particle movement is enhanced”

Does the constriction at the point of high pressure actually increase the amplitude of the corresponding frequency or does it just impede the other frequencies making it stand out more?

Thank you 🙂

[Catherine Lai]

Hi Rory,

The constriction changes what frequencies are resonant (to be higher in the case you mentioned). This means that oscillations of the air particles at that frequency get a boost in energy, which we observe as amplification. As you would see in the spectrogram, a range of frequencies around the resonance are also amplified (The black formant band actually indicates a range of frequencies are boosted).

Oscillations at frequencies that are not so close the the resonant frequency will lose energy, so their amplitudes will go to zero (unless they are boosted by something else!).
In general how sharply frequencies around the natural resonant frequency drop off depends on the “tuning” of the system (a tuning fork is much more sharply tuned than the human vocal tract!).

cheers,
Catherine

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