6.6 The Influence of Wall Material on Brass Instrument Performance
317
of results as Miller. The spectrogram in Fig. 6.26 illustrates several situations in
which the sound production of the pipe is severely modified and even extinguished.
Similar disruptive effects are sometimes observed during the manufacture of
organ pipes. An example of an organ pipe giving a quasi-periodic regime because
of a coincidence between an acoustic mode and a structural mode is described
by Nederveen and Dalmont (2004). The resulting jarring sound resulting from
the coupling of the modes can be described as a ‘wolf’, by analogy with the
similar perturbation which is caused on a bowed string instrument by a coincidence
between a powerful body resonance and the fundamental string mode. To get such
spectacular effects in wind instruments, one needs a resonator having a large internal
diameter and a thin and elastic tube with low damping. Through trial and error,
organ builders have learned to make the walls of axisymmetric metal organ pipes
sufficiently thick to avoid wolfing. Coupling between acoustic and structural modes
is more of a problem in tubes which do not have axial symmetry (see Sect. 6.6.4);
probably for this reason, square cross-section pipes of the type investigated by
Miller usually have thick wooden walls with high internal damping.
6.6.4 Frequency-Localised and Broadband Effects of
Structural Resonances in Brass Instruments
We have seen that when a brass instrument is played, it vibrates tangibly in
the player’s hands. Like any metallic structure, a brass bell has a set of lightly
damped structural modes, each mode corresponding to a specific vibrational pattern.
Taking advantage of technological advances over the last half century, many authors
have measured, visualised and calculated structural modes of brass instruments.
Experimental techniques used include holographic interferometry (Smith 1986)
and electronic speckle pattern interferometry (Moore et al. 2002), while fruitful
calculations have been performed using finite element techniques (Watkinson and
Bowsher 1982; Balasubramanian et al. 2019). Calculations and measurements (see
Fig. 6.27) show many structural modes; these usually come in pairs, with associated
eigenfrequencies and normal modal shapes which are slightly different because of
asymmetries in the system.
One axisymmetric mode is shown in more detail in Fig. 6.28. This mode,
sometimes called the piston mode, is particularly important in the context of
axisymmetric brass instrument bells, since it is the most appropriate to be coupled
with the internal acoustic field. In this mode the bell vibration consists of a periodic
expansion and contraction in the axial direction, with a single nodal plane cutting
the axis at the centre of mass. For the dimensions typical of a brass instrument bell,
the vibration amplitude is significant only very close to the bell rim, as shown by
the colour scale in Fig. 6.28.
The mechanisms of the vibroacoustic couplings involved in brass instruments are
difficult to investigate, as fluid-structure interactions are weak. To help clarify the
317
of results as Miller. The spectrogram in Fig. 6.26 illustrates several situations in
which the sound production of the pipe is severely modified and even extinguished.
Similar disruptive effects are sometimes observed during the manufacture of
organ pipes. An example of an organ pipe giving a quasi-periodic regime because
of a coincidence between an acoustic mode and a structural mode is described
by Nederveen and Dalmont (2004). The resulting jarring sound resulting from
the coupling of the modes can be described as a ‘wolf’, by analogy with the
similar perturbation which is caused on a bowed string instrument by a coincidence
between a powerful body resonance and the fundamental string mode. To get such
spectacular effects in wind instruments, one needs a resonator having a large internal
diameter and a thin and elastic tube with low damping. Through trial and error,
organ builders have learned to make the walls of axisymmetric metal organ pipes
sufficiently thick to avoid wolfing. Coupling between acoustic and structural modes
is more of a problem in tubes which do not have axial symmetry (see Sect. 6.6.4);
probably for this reason, square cross-section pipes of the type investigated by
Miller usually have thick wooden walls with high internal damping.
6.6.4 Frequency-Localised and Broadband Effects of
Structural Resonances in Brass Instruments
We have seen that when a brass instrument is played, it vibrates tangibly in
the player’s hands. Like any metallic structure, a brass bell has a set of lightly
damped structural modes, each mode corresponding to a specific vibrational pattern.
Taking advantage of technological advances over the last half century, many authors
have measured, visualised and calculated structural modes of brass instruments.
Experimental techniques used include holographic interferometry (Smith 1986)
and electronic speckle pattern interferometry (Moore et al. 2002), while fruitful
calculations have been performed using finite element techniques (Watkinson and
Bowsher 1982; Balasubramanian et al. 2019). Calculations and measurements (see
Fig. 6.27) show many structural modes; these usually come in pairs, with associated
eigenfrequencies and normal modal shapes which are slightly different because of
asymmetries in the system.
One axisymmetric mode is shown in more detail in Fig. 6.28. This mode,
sometimes called the piston mode, is particularly important in the context of
axisymmetric brass instrument bells, since it is the most appropriate to be coupled
with the internal acoustic field. In this mode the bell vibration consists of a periodic
expansion and contraction in the axial direction, with a single nodal plane cutting
the axis at the centre of mass. For the dimensions typical of a brass instrument bell,
the vibration amplitude is significant only very close to the bell rim, as shown by
the colour scale in Fig. 6.28.
The mechanisms of the vibroacoustic couplings involved in brass instruments are
difficult to investigate, as fluid-structure interactions are weak. To help clarify the