PASCO WA-9612 RESONANCE TUBE - Manual (Page 8)

Resonance Tube 012-03541E
4
Waves in a Tube Theory:
Sound Waves
When the diaphragm of a speaker vibrates, a sound
wave is produced that propagates through the air. The
sound wave consists of small motions of the air
molecules toward and away from the speaker. If you
were able to look at a small volume of air near the
speaker, you would find that the volume of air does
not move far, but rather it vibrates toward and away
from the speaker at the frequency of the speaker
vibrations. This motion is very much analogous to
waves propagating on a string. An important differ-
ence is that, if you watch a small portion of the string,
its vibrational motion is transverse to the direction of
propagation of the wave on the string. The motion of a
small volume of air in a sound wave is parallel to the
direction of propagation of the wave. Because of this,
the sound wave is called a longitudinal wave.
Another way of conceptualizing a sound wave is as a
series of compressions and rarefactions. When the
diaphragm of a speaker moves outward, the air near
the diaphragm is compressed, creating a small volume
of relatively high air pressure, a compression. This
small high pressure volume of air compresses the air
adjacent to it, which in turn compresses the air adja-
cent to it, so the high pressure propagates away from
the speaker. When the diaphragm of the speaker moves
inward, a low pressure volume of air, a rarefaction, is
created near the diaphragm. This rarefaction also
propagates away from the speaker.
In general, a sound wave propagates out in all direc-
tions from the source of the wave. However, the study
of sound waves can be simplified by restricting the
motion of propagation to one dimension, as is done
with the Resonance Tube.
Standing Waves in a Tube
Standing waves are created in a vibrating string when
a wave is reflected from an end of the string so that the
returning wave interferes with the original wave.
Standing waves also occur when a sound wave is
reflected from the end of a tube.
A standing wave on a string has nodes—points where
the string does not move—and antinodes—points
where the string vibrates up and down with a maxi-
mum amplitude. Analogously, a standing sound wave
has displacement nodes—points where the air does not
vibrate—and displacement antinodes—points where
the amplitude of the air vibration is a maximum.
Pressure nodes and antinodes also exist within the
waveform. In fact, pressure nodes occur at displace-
ment antinodes and pressure antinodes occur at
displacement nodes. This can be understood by
thinking of a pressure antinode as being located
between two displacement antinodes that vibrate 180°
out of phase with each other. When the air of the two
displacement antinodes are moving toward each other,
the pressure of the pressure antinode is a maximum.
When they are moving apart, the pressure goes to a
minimum.
Reflection of the sound wave occurs at both open and
closed tube ends. If the end of the tube is closed, the
air has nowhere to go, so a displacement node (a
pressure antinode) must exist at a closed end. If the
end of the tube is open, the pressure stays very nearly
at room pressure, so a pressure node (a displacement
antinode) exists at an open end of the tube.
Resonance
As described above, a standing wave occurs when a
wave is reflected from the end of the tube and the
return wave interferes with the original wave. How-
ever, the sound wave will actually be reflected many
times back and forth between the ends of the tube, and
all these multiple reflections will interfere together. In
general, the multiply reflected waves will not all be in
phase, and the amplitude of the wave pattern will be
small. However, at certain frequencies of oscillation,
all the reflected waves are in phase, resulting in a very
high amplitude standing wave. These frequencies are
called resonant frequencies.
In Experiment 1, the relationship between the length of
the tube and the frequencies at which resonance occurs
is investigated. It is shown that the conditions for
resonance are more easily understood in terms of the
wavelength of the wave pattern, rather than in terms of
the frequency. The resonance states also depend on
whether the ends of the tube are open or closed. For
an open tube (a tube open at both ends), resonance
occurs when the wavelength of the wave (l) satisfies
the condition:
L = nl/2, n = 1, 2, 3, 4,….
where L = tube length.
These wavelengths allow a standing wave pattern such
that a pressure node (displacement antinode) of the