First published online March 27, 2009
Journal of Experimental Biology 212, 1212-1224 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.026872
Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx
Coen P. H. Elemans1,2,*,
Mees Muller1,
Ole Næsbye Larsen2 and
Johan L. van Leeuwen1
1 Experimental Zoology Group, Wageningen University, Marijkeweg 40, NL-6709 PG
Wageningen, The Netherlands
2 Institute of Biology, University of Southern Denmark, Campusvej 55, DK-5230
Odense M, Denmark
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Fig. 1. Schematic representations of mechanical syrinx models. Models by (A)
Dürrwang (Dürrwang,
1974 ), (B) Abs (Abs,
1980), (C) Brittan-Powell et al.
(Brittan-Powell et al., 1997)
and (D) the model presented here. L, labial imitation; pd,
downstream (tracheal) pressure; pe, external (air sac)
pressure; pu, upstream (bronchial) pressure;
p1, pressure directly upstream and p2,
pressure directly downstream from membrane; R, dental cement ridge.
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Fig. 2. Schematic representation of the mechanical syrinx model (MSM): (A) frontal
and (B) lateral view. In B the clamps and shells for mounting the membrane are
shown. The rotating disc valve controls the upstream pressure
pu by closing and opening the tube inlet. The positions of
the two pressure transducers (for pe and
pu) is indicated; L, tube length; mic, location
of microphone. Between A and B, part of the rotating valve is show from
another view point to reveal its geometry.
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Fig. 3. (A) A medial section through the aluminium tube of the model showing
deflections in the membrane with increasing external pressure
(pe). Line 1 represents the membrane at resting length
(lm). With increasing pe, the membrane
deflects more into the tube lumen (curve 2). Curve 3 represents the maximal
length of the membrane during experiments. When air is flowing trough the tube
(from left to right) the membrane deforms (curve 4).
lm=10.55 mm; hm=5.6 mm. (B) To
estimate the area of the vibrating membrane, an ellipse is projected on the
tubes' casing.
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Fig. 4. Typical results from a time series of (A) sound pressure; (B) membrane
velocity, and (C) upstream pressure, pu. The arrow
indicates the pressure head that emerges from the disc valve. Rotation
frequency of airflow valve=1.6 Hz. Mean pe=5.58 kPa. (D)
Spectrogram of sound and (E) of membrane velocity.
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Fig. 5. Sound and membrane parameters as a function of upstream pressure. (A,C)
Root mean squares (r.m.s.) of sound pressure values of (A) sound pressure and
(C) membrane velocity. The arrows indicate the progression of time. The insets
show a single exemplary bin of the recorded signals with r.m.s. values. (B,D)
Fundamental frequency of (B) sound and (D) membrane velocity. The behaviour of
the membrane changes instantly from no movement to oscillation at about 750
Hz, which represents a bifurcation of this nonlinear system.
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Fig. 6. Fundamental frequency of the vibrating membrane correlates tightly with the
fundamental frequency of the produced sound (linear regression;
R2=0.97,
P 0.001,
N=2672).
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Fig. 7. (A,B) Detail of (A) sound wave and (B) membrane displacement. Single
oscillation periods of the sound pressure (grey bars) correspond to periods of
the membrane position. (C,D) Spectrum estimates of the signals shown in A and
B, respectively. Arrows indicate the fundamental frequency.
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Fig. 8. Dynamic tensile tests of the membranes M1, M2 and M3. Thick dotted lines
show the results of linear regression per membrane. The blue shaded area
indicates the estimated strain range (0.55–1.67) that occurs during
phonation, according to Fig.
3.
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Fig. 9. (A–C) Fundamental frequency in the upstream and external pressure
control space for the three different membranes M1 (A), M2 (B) and M3 (C).
Dots indicate the exact measurement locations. The colours show mean
fundamental frequency f0 of the measurements in the
specific grid cell. The bright coloured section of the colour bar shows the
range of f0 measurements. Red isolines indicate the
minimal transmural pressure needed for sound production. (D–F)
Fundamental frequency in the tension K and upstream pressure
pu control space for the three different membranes The
elliptical arrows in E indicate possible paths to create the sound syllables
(see Discussion).
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Fig. 10. Lower bound of fundamental frequency range as a function of (A) Young's
modulus and (B) mass (Table 1)
for membranes M1–3.
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Fig. 11. The effect of distal tube elongation on the frequency of the produced
sound. (A) Tube length versus the measured fundamental
(f0: closed circles) and first harmonic
(f1: open circles). The two lines show the lowest
resonance frequency (H1) of a cylinder that is,
respectively, open (solid line: Eqn
5) or closed on one end (dotted line:
Eqn 6). (B) Regression of the
measured fundamental frequency (closed circles) to estimate the end correction
 (see Results). R2=0.997, P<0.01.
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© The Company of Biologists Ltd 2009
