There are a couple of different ways of building a
Rijke Tube and they all operate will similar
principles. The most common construction is a
vertical tube with a heat source in the bottom
section of the tube.
The study of systems
like this falls within the area called "Dynamical
Systems and Control",which is rather mathematical.
However I can give you some physical intuition
about what is going on that should help with your
explanation to your students.
One way of
thinking of this is to compare your Rijke tube to
a organ pipe. Anorgan pipe has a resonant
frequency which depends on its length. When air
is forced into it the pipe resonates and we hear
the musical note. It's actually the air pressure
that is resonating here. The pipe will contain
regions of slightly higher and slightly lower
pressure in an oscillating pattern. These
pressure waves are broadcast from the pipe and
travel through the atmosphere (at the speed of
sound) to our ears. Our eardrums move in response
to these pressure variations and we sense this
movement as sound.
On the
other hand the Rijke tube experiment is not stable
in the same way. Without forcing air into it, the
oscillations build up to some level and are
sustained at that level. As in the case of a
organ pipe, it is the pressure in the air column
that is oscillating. A few other things are
oscillating as well and I'll talk about these
later.
It is the interaction between the
heat source and the acoustic characteristics of
the tube which creates this unstable response
The size of the pressure variations (which we hear
as the volume of sound) is ultimately limited by
the available energy in the heat source and how
well the heat source transfers this energy into
heating up the air around it. The frequency of
the oscillations (or musical tone) is determined
by the length of the tube,just as it is in the
organ pipe case.
We can look in more detail
at the interaction between the heat source and the
air pressure for a bit more insight. The heat
source warms the air around it, and as the warm
air rises in the tube it pushes up on colder air
above it. The rising warm air also draws more air
into to the tube past the heat source. This air
flowing past the heat source cools it down very
slightly, making slightly less heat available to
warm this new batch of air. This batch of air is
therefore cooler than the warmed air above it and
the air flow into the tube slows. With the slower
flow of air the heat source warms up again and the
cycle begins again. This leaves an oscillating
pattern of hot and cold air in the tube, and
because hot and cold air have slightly different
densities this means that we have an oscillating
pattern of pressures in the tube. This pressure
oscillation creates sound exactly like the organ
pipe.
So there are several things that
are resonating at 70 Hz in your tube. The obvious
one is the air pressure in the tube, which leads
to the sound that you hear. The preceding
discussion suggests that the temperature of the
heat source is also oscillating at 70Hz, as is
the air flow into the tube. Resonant tubes
(both Rijke tubes and organ pipes) are extremely
efficient in terms of the size of the air pressure
wave they create when they resonate. The heat
source temperature variation is probably extremely
small (perhaps a tiny fraction of a degree) which
means that you would not be able to measure it
easily. Similarly, the change in the air flow
into the pipe is also extremely small. It would be
very difficult to setup a school experiment to
measure either of these quantities. You might
consider a few modifications to your experiment to
illustrate some of these points.
- You
could try disrupting the air flow into the tube,
perhaps by constricting it in some way. This
will probably stop the oscillation if you are cut
off enough of the air supply. If your heat
source is a flame (rather than a small electric
element) then you might end up also cutting off
the oxygen supply and extinguishing the flame.
- You could also try using different heat
sources, particularly ones with different
thermal masses. To get an oscillation the
temperature of the heat source must be able to
change quickly (more precisely it must be able to
change at 70 Hz). Something with a large thermal
mass (for example an electric stove top heating
element) would probably not be able to do this.
- Change the length of your tube; making it
longer should make the note lower in
frequency.
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