Engineering Acoustics/Vocal Folds

Introduction
The mechanism of sound production in speech and singing would be the results of airflow in the human lung system, and is also connected to the digestive system. The diaphragm action from the lungs pushes air through the vocal folds, and produces a periodic train of air pulses. This pulses train is shaped by the resonances in the vocal tract, and has various frequencies and loudness. Vocal formants are basic resonances, and can be changed by the movements of the articulators to produce different vowel sounds. To produce different vowel sounds, the vocal mechanism is controlled to produce the resonances of the vocal tract is produced the vocal formants. The vocal tract can be considered to be a cavity resonator, and the soft palate position, the area of opening, the tongue positions an shape, and the position of jaw would established the shape of this cavity. More specifically, voice articulation is the movement of the tongue, pharynx palate, jaw or lips that changes the volume of cavity, area of opening, and port length, which determine the frequency of the cavity resonance. The voice mechanism can be modeled as the lung and diaphragm being the power source, along with the larynx, pharynx, mouth and nose. At the end of the tubular larynx rest the vocal folds, also known as vocal cords. During speech and singing, the larynx is connected to pharynx, and is covered by epiglottis during swallowing. The vocal tract acts as a resonator.



The vocal folds
Vocal folds are twin enfoldings of mucous membrane that act as a vibrator during phonation. Phonation is the process by which the energy from the lungs in the form of air pressure is converted vibration that is perceivable to the human ear. There are two methods to phonation. One is by the air pressure setting the elastic vocal folds into vibration, which is called voicing. The other is air passing through the larynx to vocal tract, where airstream gets modified as produces transient of aperiodic sound waves. In aperiodic phonation, the transient or aperiodic sound waves generates plosive sound, /t/, where sound is produced by blocking the airstream and suddenly releasing the built-up air pressure, fricative sound, /sh/, where a continuous noise type sounds is made by forcing air through a constricted space, affricate sound, /ch/, which is a combination of plosive and fricative sound, and a voiced consonant, /d/, which is a plosive sound followed by a voiced sound. While vocal folds are open for breathing, the folds are close by the pivoting of the arytenoid cartilages for speech of singing. Positive air pressure from the lungs forces the vocal folds to open but the high velocity air produces a lowered pressure due to the Bernoulli equation which brings them back together. In an adult male, the vocal folds are 17-23 mm long, and it is around 12.5-17 mm in an adult female. Due to the action of muscles in the larynx, the vocal folds can be stretched 3 to 4 mm. The frequency of the adult male speaking voice is typically 125 Hz, while the frequency of the adult female voice is about 210 Hz. Children’s voice is around 300 Hz. In comparison to a piano keyboard, the men’s voice would be 1 octave lower than a women’s voice, and a child’s voice would be 1 octave higher than an adult women’s voice. The front end of the vocal folds is attached to the thyroid cartilage. The back end is attached to the arytenoid cartilages, which separates the folds for breathing.

Electrical circuit representation of vocal folds
The vibration model of vocal folds, and the acoustic impedance model of the vocal can be represented as electrical circuit representation. A gyrator can be used to combine the acoustic impedance model and the vibration model, so that the velocity(as potential) from the mobility analogy for the vibration model can be transferred to the velocity(as current) in the acoustic impedance model, and where pressure would be force divided by surface area of the vocal folds tube.