3.4 Why Do the Lips Buzz?
93
Fig. 3.30 A plot of four mechanical response curves obtained with human lips, using the video
method. The played frequency for each note is marked by a vertical line. The magnitude curves
have been offset by a few dB for display purposes. Reproduced from Newton et al. (2008) with the
permission of the Acoustical Society of America
3.4 Why Do the Lips Buzz?
In Sect. 3.2 a model of the lips of a brass player as a 1DOF mechanical oscillator
was presented. The equation of motion for this oscillator was given in Eq. 3.3 as
d 2 h
dt 2 +
ω l
q l
dh
dt
+ ω
2
l (h − h eq ) =
F
m
.
The second term on the left-hand side of this equation represents the damping of the
oscillator, with the quality factor q l determining the rate at which energy of motion
is drained from the oscillator by dissipative processes. In Sect. 3.3 we have seen
that the human lip is a strongly damped oscillator, which implies that a vibration
started in the lips will die out very quickly unless the external force F is capable of
supplying energy to the mass to compensate for the damping. When a player starts
to buzz the lips, where does the energy come from to sustain the vibration?