Biomedical Engineering Reference
In-Depth Information
P , U , z
1 1 1
P , U , z
0 0 0
P , U , z
2 2 2
Fig. 7.6.
The acoustic impedance of a branching pipe
computed as a function of the frequency, and the impedances of beaks are
also discussed. A nice study of vocal-tract function in birdsong produc-
tion, with manipulation of beak movements, was presented by Hoese et al.
[Hoese et al. 2003].
It is possible to solve a source model to generate a harmonically rich sound
signal. The volume velocity can be computed, and the component of the sound
pressure associated with each harmonic component of the volume velocity can
be easily obtained by just multiplying it by the proper impedance. However, a
word of caution is needed. In this procedure we have assumed that the system
under study is linear (the passive acoustic tract), and that the nonlinear
system is uncoupled from our linear system. We are not concerned with how
the spectrally rich signal that is injected into our linear problem is generated.
But we must keep in mind that as soon as the tube and the nonlinear sound-
generating sources are
coupled
, the system as a whole is nonlinear. At this
point, direct integration of the source dynamics plus boundary conditions
is needed, since the whole concept of impedance relies on the assumption
that the forcing and the forced system will end up oscillating with the same
frequency.
With these building blocks, some very interesting problems can be ad-
dressed. Recently, Fletcher et al. [Fletcher et al. 2004] analyzed the “coo”
vocalizations of ring doves. These birds generate sounds through a mecha-
nism that differs from those described so far. They produce a vocalization that
consists basically of a pure tone of relatively low frequency (around 600 Hz).
The most remarkable aspect of this vocalization is that it is produced with the
beak and nostrils closed. While the bird produces this vocalization, it inflates
the upper part of the esophagus, and it is this “sac” what radiates the sound.
The use of impedances allowed Fletcher et al. to settle several issues. They
established the plausibility of the trachea-glottis-inflated-esophagus system
being a band-pass filter, and they showed that the inflated esophagus is a
more e
cient sound-radiating mechanism than the open beak.
