Effect of wall vibrations

(in brass wind instruments)

 

Both players and makers of brass wind instruments believe that the wall material and thickness, as well as the position of bends and braces, may affect the timbre of the instrument. While there is some truth in this statement, theoretical and experimental evidence shows that the effect of wall vibrations is more limited than originally believed. This has been verified by analysing the sound of instruments while damping the wall vibrations. In an experimental setting, this is possible, e.g., by inserting the instrument in a sandbox. In numerical simulations, wall vibrations can be simply switched on and off. In both cases, a broadband effect has been observed when damping the wall vibrations.

During performance, the acoustic pressure inside a brass instrument causes the walls to vibrate. Namely, a series of axisymmetric and elliptical modes may be excited, as shown in Figure 1. Elliptical modes normally have very high quality factors - this means that they are only excited at a specific frequency - and can not explain the effect mentioned above. On the other hand, axisymmetric (axial) modes are associated with a motion of a large part of the bell along its axis, and can be shown to affect a wider frequency range. The question remains how such a vibration may influence the sound of a wind instrument. 

According to theory, it is the geometry of the instrument bore that determines the sound of the instrument. However, as depicted in Figure 2, axial vibrations may translate into variation in the bore diameter. This, in turn, affects the acoustic pressure inside the instrument and explains the fact that, when wall vibrations are “enabled” the response of the instrument differs. This is usually assessed by measuring the input impedance of the instrument. Figure 3 shows the difference in the input impedance of an instrument with damped and free-vibrating walls measured experimentally (top) and simulated numerically (bottom). Note that this effect can be further amplified by considering:

  • the force between the player’s lips and the mouthpiece, which can further stimulate the axial wall vibrations;
  • the fact that the instrument wall is not perfectly axisymmetric; deviation from a perfectly circular cross-section diminish the local wall stiffness.

Publications

Balasubramanian, Saranya; Chatziioannou, Vasileios and Kausel, Wilfried (2019)
"Analysis of Axisymmetric Structural Vibrations in Brass Instruments,"
Acta Acustica united with Acustica 105 (3), 506-515. https://doi.org/10.3813/AAA.919332

Chatziioannou, Vasileios; Balasubramanian, Saranya and Kausel, Wilfried (2019)
"Vibroacoustic analysis of trumpet wall vibrations,"
in Proceedings of the International Congress on Sound and Vibration (ICSV26)

Kausel, Wilfried; Chatziioannou, Vasileios; Moore, Thomas R.; Gorman, Britta R., and Rokni, Michelle (2015)
"Axial vibrations of brass wind instrument bells and their acoustical influence: Theory and simulations,"
Journal of the Acoustical Society of America (JASA) 137(6), 3149–3162. https://doi.org/10.1121/1.4921270

Moore, Thomas R.; Gorman, Britta R.; Rokni, Michelle; Kausel, Wilfried, and Chatziioannou, Vasileios (2015)
"Axial vibrations of brass wind instrument bells and their acoustical influence: Experiments,"
Journal of the Acoustical Society of America (JASA) 138(2), 1233-1240. https://doi.org/10.1121/1.4928138

Gorman, Britta; Rokni, M.; Moore, Thomas; Kausel, Wilfried, and Chatziioannou, Vasileios (2014)
"Bell Vibrations and How They Affect the Sound of the Modern Trumpet,"
in Proceedings of the International Symposium on Music Acoustics, ISMA 2014 (Le Mans, France) p. 215-218.

Chatziioannou, Vasileios; Kausel, Wilfried, and Moore, Thomas (2012)
"The effect of wall vibrations on the air column inside trumpet bells,"
in Proceedings of the Acoustics 2012 Nantes Conference (Nantes, France) p. 2243-2248.

Chatziioannou, Vasileios and Kausel, Wilfried (2011)
"Modelling the wall vibrations of brass wind instruments,"
in Proceedings of the COMSOL Conference 2011 (Stuttgart).

Kausel, Wilfried; Chatziioannou, Vasileios, and Moore, Thomas R. (2011)
"More on the structural mechanics of brass wind instrument bells,"
in Forum Acusticum Aalborg 2011 (European Acoustics Association, Aalborg, Denmark) p. 527-532.

 

Figure 1. Structural bell vibrations, showing both elliptical (a & c) and axisymmetric (b & d) modes.

 

Figure 2. Vibrating brass wind instrument with bends and braces.

 

Figure 3. Difference in the input impedance of the bell caused by the wall vibrations measured experimentally (top) and calculated numerically (bottom). The dashed lines indicate the locations of the impedance peaks.