Two 3D finite element (FE) models were constructed, based on CT measurements of a subject phonating on [a:]
before and after phonation into a tube. Acoustic analysis was performed by exciting the models with acoustic
flow velocity at the vocal folds. The generated acoustic pressure of the response was computed in front of the
mouth and inside the vocal tract for both FE models. Average amplitudes of the pressure oscillations inside the
vocal tract and in front of the mouth were compared to display the cost-efficiency of sound energy transfer at
different formant frequencies. The formants F1–F3 correspond to classical vibration modes also solvable by 1D
vocal tract model. However, for higher formants, there occur more complicated transversal modes which require
3D modelling. A special attention is given to the higher frequency range (above 3.5 Hz) where transversal modes
exist between piriform sinuses and valleculae. Comparison of the pressure oscillation inside and outside the vocal
tract showed that formants differ in their efficiency, F4 (at about 3.5 kHz, i.e. at the speaker’s or singer’s formant
region) being the most effective. The higher formants created a clear formant cluster around 4 kHz after the vocal
exercise with the tube. Since the human ear is most sensitive to frequencies between 2 and 4 kHz concentration of
sound energy in this frequency region (F4–F5) is effective for communication. The results suggest that exercising
using phonation into tubes help in improving the vocal economy