326
6 Shocks and Surprises: Refining the Elementary Model
by experiments carried out by James Whitehouse et al. (2003) using artificial lips. A
simple instrument (a trombone mouthpiece coupled to a cylindrical metal pipe) was
sounded using an artificial mouth, and its wall vibrations were measured using a
laser vibrometer. A velocity amplitude of the order of 1 mm s −1 was observed at the
fundamental frequency of the sounded note (333 Hz); the corresponding operating
deflection shape resembled the shape of the second bending mode of the pipe, with
a mode frequency of 230 Hz.
To investigate the relative importance of mechanical and acoustical excitation of
the wall vibrations, two further experiments were carried out. In the first experiment,
a short piece of flexible tubing was inserted between the mouthpiece and the pipe,
greatly reducing the efficiency of the mechanical coupling of the lips to the pipe.
It was found that this reduced the amplitude of the pipe vibration by a factor of 5.
In the second experiment, the mouthpiece remained mechanically coupled to the
pipe, but the end of the mouthpiece stem was connected to a second tube inside the
pipe. The resulting removal of the acoustical pumping of the pipe had little effect
on its vibration amplitude. The main conclusion of the study was therefore that the
dominant mechanism in exciting this type of wall resonance was the motion of the
lips against the mouthpiece, rather than air pressure changes within the pipe.
The focus of Sect. 6.6.4 was on the possible effects of wall vibrations on the
sound radiated by a brass instrument. From the perspective of the listener, this
is clearly paramount. From the point of view of the performer, the story may be
rather different. The player is in contact with the vibrating instrument, most directly
through the lips pressed against the mouthpiece rim. Newton’s second law tells us
that if the lips exert an oscillating force on the mouthpiece, the mouthpiece exerts an
equal and opposite force on the lips. The sensitivity of the player to subtle vibrations
communicated through the lip-mouthpiece interface is a topic which needs much
further study. The difference between the listener and the player can be expressed in
the language of measurement technology: the listener is like a microphone, sensing
only the sound, but the player is like a microphone sensitive to the sound and also
an accelerometer sensitive to the vibrations. This could be one reason why, although
the listener may not hear any difference between two brass instruments whose
mechanical behaviour is slightly different, the player could detect these differences
by sensing the vibrations.
6.7 Going Further: Analytical Modelling of Vibroacoustic
Coupling in Ducts
Several different approaches to the modelling of the interaction between the
internal acoustic field and the wall vibrations in a brass instrument were outlined
in Sect. 6.6.4. Section 6.7 introduces an analytical approach to the theory of
vibroacoustic coupling in ducts. To illustrate the basic principles and some general
conclusions, only the simple case of a tube of uniform cross-section is considered.
It is assumed that the tube is rigidly supported and otherwise isolated from external
6 Shocks and Surprises: Refining the Elementary Model
by experiments carried out by James Whitehouse et al. (2003) using artificial lips. A
simple instrument (a trombone mouthpiece coupled to a cylindrical metal pipe) was
sounded using an artificial mouth, and its wall vibrations were measured using a
laser vibrometer. A velocity amplitude of the order of 1 mm s −1 was observed at the
fundamental frequency of the sounded note (333 Hz); the corresponding operating
deflection shape resembled the shape of the second bending mode of the pipe, with
a mode frequency of 230 Hz.
To investigate the relative importance of mechanical and acoustical excitation of
the wall vibrations, two further experiments were carried out. In the first experiment,
a short piece of flexible tubing was inserted between the mouthpiece and the pipe,
greatly reducing the efficiency of the mechanical coupling of the lips to the pipe.
It was found that this reduced the amplitude of the pipe vibration by a factor of 5.
In the second experiment, the mouthpiece remained mechanically coupled to the
pipe, but the end of the mouthpiece stem was connected to a second tube inside the
pipe. The resulting removal of the acoustical pumping of the pipe had little effect
on its vibration amplitude. The main conclusion of the study was therefore that the
dominant mechanism in exciting this type of wall resonance was the motion of the
lips against the mouthpiece, rather than air pressure changes within the pipe.
The focus of Sect. 6.6.4 was on the possible effects of wall vibrations on the
sound radiated by a brass instrument. From the perspective of the listener, this
is clearly paramount. From the point of view of the performer, the story may be
rather different. The player is in contact with the vibrating instrument, most directly
through the lips pressed against the mouthpiece rim. Newton’s second law tells us
that if the lips exert an oscillating force on the mouthpiece, the mouthpiece exerts an
equal and opposite force on the lips. The sensitivity of the player to subtle vibrations
communicated through the lip-mouthpiece interface is a topic which needs much
further study. The difference between the listener and the player can be expressed in
the language of measurement technology: the listener is like a microphone, sensing
only the sound, but the player is like a microphone sensitive to the sound and also
an accelerometer sensitive to the vibrations. This could be one reason why, although
the listener may not hear any difference between two brass instruments whose
mechanical behaviour is slightly different, the player could detect these differences
by sensing the vibrations.
6.7 Going Further: Analytical Modelling of Vibroacoustic
Coupling in Ducts
Several different approaches to the modelling of the interaction between the
internal acoustic field and the wall vibrations in a brass instrument were outlined
in Sect. 6.6.4. Section 6.7 introduces an analytical approach to the theory of
vibroacoustic coupling in ducts. To illustrate the basic principles and some general
conclusions, only the simple case of a tube of uniform cross-section is considered.
It is assumed that the tube is rigidly supported and otherwise isolated from external