334
6 Shocks and Surprises: Refining the Elementary Model
This device, making it possible to satisfy exactly the frequency coincidence or,
on the contrary, to avoid it, was connected to a clarinet mouthpiece in an artificial
mouth. The length of the thin-walled plastic section was 24 cm, and the additional
lengths of the rigid slide in open position and the mouthpiece inside the artificial
mouth gave a sounding length of about 50 cm. The experimental setup thus had a set
of fixed mechanical modes and a set of variable acoustic modes. The second acoustic
resonance frequency could be adjusted between 400 Hz and 550 Hz by moving the
slide, allowing upward and downward glissandi to be played.
With the slide at its minimum length, a periodic regime corresponding to the
normal clarinet functioning on its second natural note was obtained. As the slide was
pulled slowly outwards, the fundamental frequency of the periodic regime decreased
until a crucial point (around the middle of the slide) was reached, at which point
a bifurcation towards a quasi-periodic regime was obtained. The resulting sound
resembled the ‘wolf note’ described in 6.6.3. When the slide was further extended,
the periodic regime was re-established. Similar behaviour was observed in upward
glissandi. Since the sounding mechanism was an artificial mouth, the phenomena
were very reproducible.
It was demonstrated by Nief et al. (2008) that the bifurcation was obtained when
the coincidence occurred between the first ovalling mechanical mode and the second
acoustic mode. As a consequence of the coincidence, the input impedance Z was
drastically perturbed, the second peak being split into two peaks.
To bring the experimental conditions a little closer to those in a real brass
instrument, the same kind of experiment was carried out with a sliding brass
cylindrical tube in place of the plastic one (Fig. 6.40). The material parameters of
brass are E = 110 GPa, ρ s = 8700 kg/m 3 and ν = 0.3. According to Eq. 6.48,
the only free parameter in determining the frequency of the first ovalling mode is
the thickness h. A thickness of h = 0.2 mm gives a first ovalling frequency of
1630 Hz, which is in the vicinity of the fifth acoustic resonance. The vibrating tube
was therefore made from brass tubing used in musical instrument making, carefully
machined to a thickness of about 0.2 mm.
The theoretical prediction that a significant disturbance of the input impedance
would occur if the tube was slightly oval was confirmed by experiment. The
measured perturbation of the input impedance could be suppressed by pinching the
tube between the fingers, and the corresponding harmonic (the fifth) was sufficiently
altered to give an audible modification of the tone colour.
The work summarised above, described in detail in Nief et al. (2008), has clearly
established a theory of vibroacoustic coupling of a vibrating cylindrical tube and its
inner air. It has been shown that a coincidence between an acoustic mode and an
ovalling mechanical modes can perturb the input impedance of the tube, modifying
the self-sustained oscillation of a clarinet-like instrument, although audible effects in
cylindrical tubes are found only for wall thicknesses much smaller than those used
in normal brass instruments. A full vibroacoustic theory dealing with the flaring
bells found on many brass instruments is not yet available.
6 Shocks and Surprises: Refining the Elementary Model
This device, making it possible to satisfy exactly the frequency coincidence or,
on the contrary, to avoid it, was connected to a clarinet mouthpiece in an artificial
mouth. The length of the thin-walled plastic section was 24 cm, and the additional
lengths of the rigid slide in open position and the mouthpiece inside the artificial
mouth gave a sounding length of about 50 cm. The experimental setup thus had a set
of fixed mechanical modes and a set of variable acoustic modes. The second acoustic
resonance frequency could be adjusted between 400 Hz and 550 Hz by moving the
slide, allowing upward and downward glissandi to be played.
With the slide at its minimum length, a periodic regime corresponding to the
normal clarinet functioning on its second natural note was obtained. As the slide was
pulled slowly outwards, the fundamental frequency of the periodic regime decreased
until a crucial point (around the middle of the slide) was reached, at which point
a bifurcation towards a quasi-periodic regime was obtained. The resulting sound
resembled the ‘wolf note’ described in 6.6.3. When the slide was further extended,
the periodic regime was re-established. Similar behaviour was observed in upward
glissandi. Since the sounding mechanism was an artificial mouth, the phenomena
were very reproducible.
It was demonstrated by Nief et al. (2008) that the bifurcation was obtained when
the coincidence occurred between the first ovalling mechanical mode and the second
acoustic mode. As a consequence of the coincidence, the input impedance Z was
drastically perturbed, the second peak being split into two peaks.
To bring the experimental conditions a little closer to those in a real brass
instrument, the same kind of experiment was carried out with a sliding brass
cylindrical tube in place of the plastic one (Fig. 6.40). The material parameters of
brass are E = 110 GPa, ρ s = 8700 kg/m 3 and ν = 0.3. According to Eq. 6.48,
the only free parameter in determining the frequency of the first ovalling mode is
the thickness h. A thickness of h = 0.2 mm gives a first ovalling frequency of
1630 Hz, which is in the vicinity of the fifth acoustic resonance. The vibrating tube
was therefore made from brass tubing used in musical instrument making, carefully
machined to a thickness of about 0.2 mm.
The theoretical prediction that a significant disturbance of the input impedance
would occur if the tube was slightly oval was confirmed by experiment. The
measured perturbation of the input impedance could be suppressed by pinching the
tube between the fingers, and the corresponding harmonic (the fifth) was sufficiently
altered to give an audible modification of the tone colour.
The work summarised above, described in detail in Nief et al. (2008), has clearly
established a theory of vibroacoustic coupling of a vibrating cylindrical tube and its
inner air. It has been shown that a coincidence between an acoustic mode and an
ovalling mechanical modes can perturb the input impedance of the tube, modifying
the self-sustained oscillation of a clarinet-like instrument, although audible effects in
cylindrical tubes are found only for wall thicknesses much smaller than those used
in normal brass instruments. A full vibroacoustic theory dealing with the flaring
bells found on many brass instruments is not yet available.