Physicists at King's College in London (Barbara Forbes, firstname.lastname@example.org)
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
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.)