Part II
Acoustical Modelling of Brasswinds
Part II consists of four chapters which review in detail the physics underlying a
performance on a brass instrument. The buzzing lips of the player, which are the
source of the sound, are discussed in Chap. 3. Propagation of acoustic waves within
the bore of the instrument and into the surrounding space is the principal topic of
Chap. 4. The theoretical development in these two chapters is based on several
approximations: propagation of sound waves inside the bore of the instrument
is described using linear acoustics, resonances of the player’s windway are not
taken into account and the walls of the instrument are assumed to be perfectly
rigid. Accepting these approximations allows us to derive an elementary model
of a brass instrument under playing conditions, which is presented in Chap. 5. In
this chapter, periodic solutions of the model are discussed, making use in part of
a nonlinear dynamical system representation. In Chap. 6, the approximations are
challenged, leading to some important refinements of the model. The theory of
nonlinear propagation is presented in order to explain the brassy character of brass
instruments under loud playing, the role of resonances of the player’s windway in
performance is discussed, and the influence of wall vibrations on the radiated sound
and the perception of the performer are addressed.
Acoustical Modelling of Brasswinds
Part II consists of four chapters which review in detail the physics underlying a
performance on a brass instrument. The buzzing lips of the player, which are the
source of the sound, are discussed in Chap. 3. Propagation of acoustic waves within
the bore of the instrument and into the surrounding space is the principal topic of
Chap. 4. The theoretical development in these two chapters is based on several
approximations: propagation of sound waves inside the bore of the instrument
is described using linear acoustics, resonances of the player’s windway are not
taken into account and the walls of the instrument are assumed to be perfectly
rigid. Accepting these approximations allows us to derive an elementary model
of a brass instrument under playing conditions, which is presented in Chap. 5. In
this chapter, periodic solutions of the model are discussed, making use in part of
a nonlinear dynamical system representation. In Chap. 6, the approximations are
challenged, leading to some important refinements of the model. The theory of
nonlinear propagation is presented in order to explain the brassy character of brass
instruments under loud playing, the role of resonances of the player’s windway in
performance is discussed, and the influence of wall vibrations on the radiated sound
and the perception of the performer are addressed.