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3 Buzzing Lips: Sound Generation in Brass Instruments
A constant force cannot play this role, since the work W done by a force F acting
in the +y direction on a mass moving with speed v in the same direction is
W = F v.
(3.17)
For the half cycle of the vibration in which the mass is moving in the +y direction,
the force will contribute energy; the same amount of energy will however be taken
away in the other half of the cycle, when F and v are in opposite directions.
When the air flow from the lip channel enters the mouthpiece of a musical
instrument, and the natural frequency of the lips is close to an acoustic resonance of
the instrument, even a small oscillating air flow can build up a powerful standing
wave in the instrument’s air column. The resulting oscillating pressure in the
mouthpiece can provide the source of energy to sustain the lip vibration provided
that the correct phase relationship is established between the lip motion and the
mouthpiece pressure. How this is achieved is explained in detail in Chap. 5.
The ability of brass players to buzz the lips freely without a mouthpiece shows
that it is possible to sustain lip vibration even without feedback from a downstream
acoustic resonator. One possible source of energy is the upstream resonance in
the player’s mouth and vocal tract. In the simple model, it is assumed that the
fluctuating air flow through the mouth creates a negligible pressure oscillation at the
upstream side of the lip channel. The circumstances in which upstream resonances
can become significant in brass playing are discussed in Sect. 6.3.
There are several other possible processes by which energy could be supplied to
sustain lip vibration without either downstream or upstream acoustic feedback, but
these take us beyond the simple 1DOF lip model. One such mechanism is a periodic
change in the profile of the lip channel. In Fig. 3.32 the lip channel is assumed to
have a height which at any given time in the vibration cycle does not vary along
the z axis (the flow direction). It is also assumed that the flow is uniform along the
lip channel. A consequence of these assumptions is that if there is no downstream
resonator, the lip channel pressure is also uniform and equal to atmospheric pressure.
This will not change during the vibration cycle, and there will therefore be no
fluctuating force on the lip which could supply energy to compensate for internal
damping.
If, however, the lip channel has a converging profile, as shown in Fig. 3.31a, the
pressure will decrease along the channel in the +z direction, reaching atmospheric
pressure only at the exit. There will then be a net upward force on the upper lip. If
the channel remained convergent throughout the vibration cycle, the direction of the
force would remain upward, and there would be no net transfer of energy to the lip.
If however the channel became divergent as the lip started to move downward, as
shown in Fig. 3.31b, the pressure would drop below atmospheric at the lip channel
entrance, and there would be a net downward force in the same direction as the lip
velocity. Energy would then be transferred to the lip in both halves of the cycle,
giving the positive feedback necessary to sustain the vibration. It is not necessary
that the switch from convergent to divergent should occur exactly at the change of
3 Buzzing Lips: Sound Generation in Brass Instruments
A constant force cannot play this role, since the work W done by a force F acting
in the +y direction on a mass moving with speed v in the same direction is
W = F v.
(3.17)
For the half cycle of the vibration in which the mass is moving in the +y direction,
the force will contribute energy; the same amount of energy will however be taken
away in the other half of the cycle, when F and v are in opposite directions.
When the air flow from the lip channel enters the mouthpiece of a musical
instrument, and the natural frequency of the lips is close to an acoustic resonance of
the instrument, even a small oscillating air flow can build up a powerful standing
wave in the instrument’s air column. The resulting oscillating pressure in the
mouthpiece can provide the source of energy to sustain the lip vibration provided
that the correct phase relationship is established between the lip motion and the
mouthpiece pressure. How this is achieved is explained in detail in Chap. 5.
The ability of brass players to buzz the lips freely without a mouthpiece shows
that it is possible to sustain lip vibration even without feedback from a downstream
acoustic resonator. One possible source of energy is the upstream resonance in
the player’s mouth and vocal tract. In the simple model, it is assumed that the
fluctuating air flow through the mouth creates a negligible pressure oscillation at the
upstream side of the lip channel. The circumstances in which upstream resonances
can become significant in brass playing are discussed in Sect. 6.3.
There are several other possible processes by which energy could be supplied to
sustain lip vibration without either downstream or upstream acoustic feedback, but
these take us beyond the simple 1DOF lip model. One such mechanism is a periodic
change in the profile of the lip channel. In Fig. 3.32 the lip channel is assumed to
have a height which at any given time in the vibration cycle does not vary along
the z axis (the flow direction). It is also assumed that the flow is uniform along the
lip channel. A consequence of these assumptions is that if there is no downstream
resonator, the lip channel pressure is also uniform and equal to atmospheric pressure.
This will not change during the vibration cycle, and there will therefore be no
fluctuating force on the lip which could supply energy to compensate for internal
damping.
If, however, the lip channel has a converging profile, as shown in Fig. 3.31a, the
pressure will decrease along the channel in the +z direction, reaching atmospheric
pressure only at the exit. There will then be a net upward force on the upper lip. If
the channel remained convergent throughout the vibration cycle, the direction of the
force would remain upward, and there would be no net transfer of energy to the lip.
If however the channel became divergent as the lip started to move downward, as
shown in Fig. 3.31b, the pressure would drop below atmospheric at the lip channel
entrance, and there would be a net downward force in the same direction as the lip
velocity. Energy would then be transferred to the lip in both halves of the cycle,
giving the positive feedback necessary to sustain the vibration. It is not necessary
that the switch from convergent to divergent should occur exactly at the change of