The acoustic structure of resonant sounds within the vocal tract can be derived from the model of the vocal tract as a uniform tube with F1, F2, F3 identified as standing waves in the tube, plus a ``rule of thumb'' which shows how formant frequencies may vary from this norm according to the location and degree of constrictions distributed along the tube. This rule predates modern phonetics; it is much older than the spectrograph machine. Fant (1960) found it in Chiba (1941), but it was originally stated by Lord Rayleigh, about a century ago. The rule predicts in a detailed way many of the basic results of acoustic phonetics which were discovered much later, results which even today seem qualitatively mysterious. This acoustic rule has rarely2.7 been used to explain basic facts in acoustic phonetics, which as we will see in this chapter, it can do quite accurately and successfully.
The rule expresses the effect on standing wave frequencies of constrictions in an acoustic tube, relative to the nodes and antinodes of the standing wave concerned. Given a lossless, uniform acoustic tube and a particular standing wave resonance in it:
At a velocity node: If the tube is constricted in the vicinity of a node of the standing wave, the frequency of the standing wave rises. Conversely, if the tube is widened in the vicinity of a node, its frequency falls.
At an antinode: If the tube is constricted in the vicinity of an antinode of the standing wave, the frequency falls. Conversely, if the tube is widened in the vicinity of an antinode, the frequency rises.
These principles are worth memorizing. The effects at nodes are opposite to the effects at antinodes, and the effects of constriction and widening are opposite to each other. Thus all that must be remembered is that antinode constriction lowers standing-wave frequency, and the other three combinations can be derived from this one.
Fant does not explain these principles, but states that they follow from elementary considerations of electrical circuit theory (chapter 1.4). The explanation appears to rely on a decrease or increase in the speed of sound due to a constriction at the location of a antinode or node, respectively.