100
3 Buzzing Lips: Sound Generation in Brass Instruments
the lips will also be modulated sinusoidally. If the amplitude of lip vibration is high
enough that the lip channel closes for part of the vibration cycle, the flow leaving
the lips will not be sinusoidal but will have additional harmonic components.
From Eq. 3.28, the flow rate from a lip buzz into open air is also proportional
to the square root of the mouth pressure. As a quantitative example, if the player
buzzes with a mouth pressure p m = 1 kPa, and the lip open area varies sinusoidally
between 0 and 20 mm 2 , Eq. 3.28 predicts that the flow rate leaving the lips will also
vary sinusoidally between 0 and 0.8 L s −1 . The maximum particle velocity of the air
at the exit to the lip channel will be just over 40 m s −1 .
When the fluctuating air flow emerges from the lip channel into the mouthpiece
of a brass instrument, the pressure p in Eq. 3.27 is no longer equal to 0, but instead
fluctuates with an amplitude and phase which depend on the acoustical properties of
the instrument. In Chap. 4 these properties are described in detail. The construction
of an elementary global brass instrument model which includes the feedback loop
which couples the buzzing lips to the acoustic resonances of the instrument is
presented in Chap. 5.
3 Buzzing Lips: Sound Generation in Brass Instruments
the lips will also be modulated sinusoidally. If the amplitude of lip vibration is high
enough that the lip channel closes for part of the vibration cycle, the flow leaving
the lips will not be sinusoidal but will have additional harmonic components.
From Eq. 3.28, the flow rate from a lip buzz into open air is also proportional
to the square root of the mouth pressure. As a quantitative example, if the player
buzzes with a mouth pressure p m = 1 kPa, and the lip open area varies sinusoidally
between 0 and 20 mm 2 , Eq. 3.28 predicts that the flow rate leaving the lips will also
vary sinusoidally between 0 and 0.8 L s −1 . The maximum particle velocity of the air
at the exit to the lip channel will be just over 40 m s −1 .
When the fluctuating air flow emerges from the lip channel into the mouthpiece
of a brass instrument, the pressure p in Eq. 3.27 is no longer equal to 0, but instead
fluctuates with an amplitude and phase which depend on the acoustical properties of
the instrument. In Chap. 4 these properties are described in detail. The construction
of an elementary global brass instrument model which includes the feedback loop
which couples the buzzing lips to the acoustic resonances of the instrument is
presented in Chap. 5.