Speech Science Sings a New Quantum Tune

Physicists at King's College in London (Barbara Forbes, forbes@phonologica.com) have devised the most precise way yet of reproducing the natural resonance frequencies, or formants, of the human vocal tract. To achieve this, they apply the methods of wave mechanics, more usually associated with quantum physics, to a classical acoustics problem for the first time. Their results may lead to better speech recognition devices, which currently do not take vocal tract physics into account and can't adapt to natural human speech styles, such as ordinary conversation.

In their paper, the researchers analyze a simple organ pipe, which speech researchers often study to gain basic insights into sound production in the vocal tract. The researchers show that adding curvatures--dents or bumps--at optimal positions in a straight organ pipe allows its natural resonance frequencies to be shifted up or down, largely independently of each other.

The analysis substantially advances a long-held 1878 result of Lord Rayleigh. Using the tools of classical physics, Rayleigh concluded that constricting an organ pipe at an antinode (region of maximum air pressure) raised its resonance frequency while expanding the pipe lowered it.

To simplify his analysis, he assumed that denting or expanding the pipe would not change two key quantities of the air inside it: the kinetic energy density (related to the average velocity of air particles) and the potential energy density (essentially the air's degree of compression, proportional to the square of the air pressure). Because of this assumption, Rayleigh could not take into account wave dispersion, in which a pulse of sound (typically made of many sinusoidal waves each of a different frequency) changes its shape as it passes through a region of pipe where the wall is dented.

In the new quantum-mechanics-based analysis, the researchers are able to model this wave dispersion. To do so, they examine how changing the pipe cross-section alters the potential energy density of the air in the vicinity of the dented pipe. Of course, the acoustical system is a macroscopic physical system and the wave functions within a pipe are real, measurable quantities. Therefore, quantum phenomena involving uncertainty and probability do not arise in the acoustical case.

In their analysis, their biggest surprise was to find, contra Rayleigh, that constricting the pipe exactly at a node (region of minimum air pressure) does not make any contribution to shifting a resonance frequency. Instead, wave phenomena in the vicinity of the node cause the shifts.

Since vowels in human speech can be distinguished by the relative positions of the vowel's 2-3 lowermost resonance frequencies (formants), this finding may provide a more sophisticated understanding of the physical phenomena that create the characteristic sets of frequencies for all phonetic sounds.

In addition, the researchers' more precise knowledge of the adjustments that can alter a pipe's resonance frequencies may provide a very robust and efficient way of programming a machine to recognize natural phonetic sounds, a line of research they are currently pursuing. They also intend to apply their method to a structure that more closely approximates the physiological conditions in the vocal tract. (Forbes and Pike, Physical Review Letters, 30 July 2004.)