322
6 Shocks and Surprises: Refining the Elementary Model
0
-10
-20
-30
Transfer Funtion (dB)
0
1000
2000
Frequency (Hz)
0
1000
2000
Frequency (Hz)
0
1000
2000
Frequency (Hz)
Frequency (Hz)
bell free
bell damped
bell free
bell damped
Difference in Transfer Function (dB)
(damped-free)
2
0
-2
0
1000
2000
120
100
80
60
40
20
0
Input Impedance (MW)
Difference in input impedancee (MW)
(damped-free)
6
4
2
0
-2
-4
-6
(a)
(b)
(c)
(d)
Fig. 6.32 (a) Transmission of the trumpet measured at the output plane of the bell plotted as a
function of driving frequency. Solid line: bell free. Dashed line: bell damped. (b) Difference in
transmission produced by damping bell vibrations. (c) Input impedance of the trumpet. Solid line:
bell free. Dashed line: bell damped. (d) Difference in input impedance produced by damping bell
vibrations. Reproduced from Kausel et al. (2010) with the permission of the Acoustical Society of
America
piston mode, has been proposed (Kausel et al. 2015). Finite element and finite
difference calculations have been shown to be capable of reproducing the main
features of the experimental measurements (Moore et al. 2015), but the material
damping coefficient required is a factor of 50 greater than that expected for brass.
There is thus as yet no totally satisfying model to interpret the experimentally
observed broadband frequency dependence of wall vibration effects, and further
research in this area is required.
A study of the effect of wall damping on a brass instrument bell has also been
undertaken by Gautier et al. (2013). Inspired by the Miller (1909) experiment
described in Sect. 6.6.3, François Gautier and colleagues at the University of
Le Mans used a water tank surrounding a trombone bell which could be filled
progressively in order to modify the mechanical modes of the bell in a continuous
manner (see Fig. 6.33). The bell was excited in turn by a loudspeaker and a
mechanical shaker. The acoustical and mechanical responses were measured for
different levels of water, allowing an analysis of the vibroacoustic couplings. The
measurements demonstrated that the vibrational modes of the bell were excited by
the internal acoustic field, but did not lead to significant changes in the radiated
6 Shocks and Surprises: Refining the Elementary Model
0
-10
-20
-30
Transfer Funtion (dB)
0
1000
2000
Frequency (Hz)
0
1000
2000
Frequency (Hz)
0
1000
2000
Frequency (Hz)
Frequency (Hz)
bell free
bell damped
bell free
bell damped
Difference in Transfer Function (dB)
(damped-free)
2
0
-2
0
1000
2000
120
100
80
60
40
20
0
Input Impedance (MW)
Difference in input impedancee (MW)
(damped-free)
6
4
2
0
-2
-4
-6
(a)
(b)
(c)
(d)
Fig. 6.32 (a) Transmission of the trumpet measured at the output plane of the bell plotted as a
function of driving frequency. Solid line: bell free. Dashed line: bell damped. (b) Difference in
transmission produced by damping bell vibrations. (c) Input impedance of the trumpet. Solid line:
bell free. Dashed line: bell damped. (d) Difference in input impedance produced by damping bell
vibrations. Reproduced from Kausel et al. (2010) with the permission of the Acoustical Society of
America
piston mode, has been proposed (Kausel et al. 2015). Finite element and finite
difference calculations have been shown to be capable of reproducing the main
features of the experimental measurements (Moore et al. 2015), but the material
damping coefficient required is a factor of 50 greater than that expected for brass.
There is thus as yet no totally satisfying model to interpret the experimentally
observed broadband frequency dependence of wall vibration effects, and further
research in this area is required.
A study of the effect of wall damping on a brass instrument bell has also been
undertaken by Gautier et al. (2013). Inspired by the Miller (1909) experiment
described in Sect. 6.6.3, François Gautier and colleagues at the University of
Le Mans used a water tank surrounding a trombone bell which could be filled
progressively in order to modify the mechanical modes of the bell in a continuous
manner (see Fig. 6.33). The bell was excited in turn by a loudspeaker and a
mechanical shaker. The acoustical and mechanical responses were measured for
different levels of water, allowing an analysis of the vibroacoustic couplings. The
measurements demonstrated that the vibrational modes of the bell were excited by
the internal acoustic field, but did not lead to significant changes in the radiated