Resonance

• The general principle of resonance is that when a periodic vibration is applied to an elastic system, the system will respond with greater amplitude of vibration the closer the applied frequencies are to the natural frequencies of the so-called resonator. Natural frequencies are those frequencies at which an object vibrates most efficiently. (Example of the porch swing. Example of a clothesline rope.)
• As applied to speech sounds and in particular voicing, the principle of resonance can be restated as follows: the length and shape of the vocal tract at any moment in time will determine which of the broad range of frequencies supplied by the glottal pulse emerge from the mouth with high amplitudes, and which with low amplitudes.
• A simple calculation can give us an idea of what the natural frequencies of the vocal tract are. The length of the tract from the glottis to the lips is about 17 cm in an adult male.
• Acoustic theory says that if we imagine the vocal tract to be a cylindrical tube of constant diameter, the natural resonance frequencies will be those for which the vocal tract length is an odd multiple of one quarter of the total wavelength, i.e. 1/4, 3/4, 5/4, ...
• The first such resonant frequency will have a wavelength four times the vocal tract length. 17 cm x 4equals 68 cm, the wavelength of the sound wave emitted by our calculation, and by a happy coincidence, the speed of sound in air at C. is 340 m/s, giving us a nice round predicted first resonant frequency value of 500 Hz.
• Similar reasoning will place the next two bands at 1500 Hz and at 2500 Hz. In fact, the most neutral vowel in American English is the schwa, and this vowel comes very close to having the formant frequencies predicted by acoustics. (Figure 6, relation to Figures 4 and 5)
• One point which it is important to grasp is that the size and shape of the mouth imprints its characteristic frequency pattern on the speaker's glottal pulse no matter what the current pitch may be. (Figure 7).
• For each voiced phoneme, a speaker adjusts the relative diameter of the tube at different points along its length by muscular activity, from the tightening of the pharyngeal walls to the pursing of the lips. In addition to this variation in tube size, the tongue can be placed into a number of different positions dividing the vocal tract into two or more sequential chambers of varying size and shape. Figure 8 shows the spectra of two actual vowels in American English.
• The muscular adjustments to the vocal tract allow us to select those frequencies which are permitted to leave the mouth and nose with almost as much power as they possess in the spectrum of the glottal pulse, and which frequencies tend to be eliminated from the speech spectrum. We select a given set of frequencies by moving our articulators into the corresponding configuration.