Vocal Tract Measurement

The vocal tract is like the internet: a series of tubes. For central vowels, we can model the vocal tract as a simple tube, like a cylinder that starts at the vocal tract and ends at the lips.

\( \begin{aligned} F_n &= \frac{(2n - 1)c}{4l} \end{aligned} \)

where

\( \begin{aligned} c &= \text{speed of sound (m/s)} \\ l &= \text{length of simple tube (m)} \\

In a vocal tract, the speed of sound is about 350 m/s. So...

\( \begin{aligned} l &= \frac{350(2n - 1)}{4F_n} \\ \end{aligned} \)

Estimate height from vocal tract length:

\( \begin{aligned} H &= 7l + 0.55 \, \text{(m)} \\ \end{aligned} \)

Activity: Guess Who

Match the speaker with the spectrogram (A-G), using vocal tract length estimation and given height. You can download the audio here.

Sara 1.625 m Audio file: ______ Est VTL: ______	Trang 1.675 m Audio file: ______ Est VTL: ______	Wesley 1.88 m Audio file: ______ Est VTL: ______	Ellen 1.625 m Audio file: ______ Est VTL: ______
Leanne 1.59 m Audio file: ______ Est VTL: ______	Juvenile 1 1.675 m Audio file: ______ Est VTL: ______	Juvenile 2 1.675 m Audio file: ______ Est VTL: ______	You ? Audio file: ______ Est VTL: ______

Some good references:

• https://www.isca-speech.org/archive/archive_papers/interspeech_2005/i05_1989.pdf
• https://www.researchgate.net/post/How_can_I_estimate_a_persons_vocal_tract_length_using_a_recorded_audio_file
• https://www.konan-u.ac.jp/hp/kitlab/pub/is2012_poster.pdf
• http://www.phon.ox.ac.uk/jcoleman/tube_models.htm
• http://www.phon.ox.ac.uk/jcoleman/tube_models2.htm