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Re: [Phys-L] The resonance phenomenon in an open ended cylindrical tube



On 01/12/2015 11:58 AM, Bill Nettles wrote:

At the risk being rebuffed, I would suggest that the "information"
carried by the sound wave is in the pressure depiction. Consider two
sources (speakers) which are distance L apart and driven by a common
source. Place a detector/microphone directly between the speakers at
L/2. Ignore reflected waves; consider only direct waves. Would you
detect no sound or maximum sound? Many students say none because
they are thinking displacement waves and the displacements cancel.
The experiment (as best as I can do it in the intro lab) says maximum
indicating to me that the pressure is the better thing to consider
for a sound wave. This conclusion is supported by a minimum when I
move the microphone to a pressure node/displacement antinode.

I would rebut that by saying it's a choice, not a law
of physics. If you /choose/ a microphone that responds
to pressure, you reach the conclusion expressed above.

You can choose what you like, but other folks are free
to choose differently. One can easily imagine detectors
that respond to velocity rather than pressure ... basically
a quick-acting anemometer.
-- A hot-wire anemometer responds to mass flux, which is
a weird combination of velocity and pressure.
-- Laser doppler will give you excellent velocity data.

Note that there is generally *more* information in the velocity
than in the pressure, because it's a vector. (In one dimension,
the amount of information is roughly the same.)

A magic word here is "microflown"
https://www.google.com/search?q=%22microflown%22

==================================

On 01/12/2015 11:31 AM, I wrote:

There should be a way to visualize this with
mechanical waves

It's hard to do with strings, but doable with torsion waves.
We want to keep the speed the same and change the impedance.
medium #1: compliant torsion member and low-inertia bars
medium #2: stiff torsion member and high-inertia bars.

Here's a picture of the whole thing, including an optional
impedance matching transition element:
https://lecdem.physics.umd.edu/g/g3/g3-07.html

For the high-tech version, this typically has a metal torsion
element and welded-on ribs. You can pick torsional spring
constant, largely by picking the diameter of the torsion element.
I'm not quite sure how to make the tapered transition section.

For the low-tech home-made version: This typically uses tape
under tension as the torsion element. Use narrow tape for medium
#1 and wide tape for medium #2.

In all cases you can increase the moment of inertia of the
ribs by making them longer and/or putting heavier bobs on
the ends. As always, it's the integral of r^2 dm.