Perceptual Coherence : Hearing and Seeing

342 Perceptual Coherence
motion of individual regions of the plate, and we can imagine the vibration
modes of a hollow tube as the motion of slugs of air within that tube
(Benade, 1960). The vibration modes of strings and plates are standing
waves that result from the summation of traveling waves reflected from the
ends of the strings and plates. The same is true for the vibratory modes of a
hollow tube. The excitation at one end of the tube produces regions of
higher pressure (compressions) and regions of lower pressure (rarefactions)
that travel down the tube and are reflected back up the tube at the other end.
At a closed end, compression and rarefaction are reflected back as compression
and rarefaction respectively (it is an antinode); at an open end,
compression is reflected back as rarefaction and vice versa (it is a node). It
takes four trips up and down the pipe to complete one cycle, so that the
wavelength of the first vibratory mode (i.e., the fundamental) is four times
the pipe length. The traveling waves sum to produce a standing wave
within the tube.
For a tube open at one end, the stronger vibration modes can occur only
at the odd vibration modes (i.e., 3F 0, 5F 0, 7F 0, 9F 0) because there must be
zero net pressure at the open end and maximum pressure variation at the
closed end. However, if the open end of the tube is flared out to create a
cone, then all vibratory modes are possible.
Source Excitation
For brass instruments, the player’s tensed lips inject puffs of air when
the oscillating air pressure at the mouthpiece is at a maximum. For woodwind
instruments, the reed acts to inject air puffs when the oscillating air
pressure at the mouthpiece is at a maximum (the lips and mouthpiece are
antinodes—regions of maximum pressure variation). The feedback from
the reflected pressure wave is critically important to stabilize the lip vibrations
for the brass instruments and to open and close the reed mouthpiece
for the woodwinds. However, it may take several round trips before the reflections
build up to the point that the lip reed vibrations become stable.
During that initiation time there are often variations in pitch and inharmonic
blips of energy.
Changing lip tension and the amplitude of the blowing pressure varies
the frequency spectrum of the airflow entering the instrument. When the instrumentalist
is blowing softly, the lips and reed will oscillate gently. The
air is never completely shut off, and the input is almost purely sinusoidal.
As the pressure is increased, the lips and reed will undergo large movements.
The air may not be completely shut off though, and the amplitudes
of the higher harmonics increase. Finally, at the highest blowing pressures,
the lips and reed snap shut and stop the airflow for up to 50% of the cycle.