Download So Just exactly is that node thing?

What the heck is a node,
anyway?????
September 26, 2005
So far we have discussed
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A little music physics
Tones
Waves
Frequencies
Wavelengths
Standing Waves
Some musical Instruments
BUT
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….
We really haven’t much discussed
We HAVE mentioned that
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Sound travels through the air.
Sound is a “pressure” wave.
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We discussed pressure (force/unit area)
Normal Atmospheric Pressure (14 psi or
101,300 Pa [N/m2] or 1 bar)
Sound travels at about 1100 ft/sec or 344
m/sec.
A loud sound represents a pressure of only
1/10,000th of an atmosphere.
Speed of sound is affected by
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Temperature
Humidity (Very Slight)
Density of the gas (air)
Temperature
(Check my Arithmetic, please)
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The speed of sound increases by 1.1 ft/sec
for every Fahrenheit degree of increased
temperature.
For a tube open at both ends, the
fundamental frequency was shown to be:
v/2L. A 100 change will produce a
corresponding frequency change of 11/1100
~ .001. For f=440, this is about ½ Hz.
A bigger temperature change would be
noticed by a trained musician.
Larger temperature excursions are possible.
Gas
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We model a gas as a collection of
spheres that are contained (usually) in
a volume and that bump into each
other from time to time.
A pressure wave increases (or
decreases) the density of these
spheres.
An Impulse Pressure Wave
Moving along
~v
Process Repeats Itself …..
A Sound Wave is Born
Fork is compressing the gas
Fork is expanding the gas
SOUND
etc.
Oh where, oh where has my
sound wave gone …
Here?
To be continued.
It eventually gets someplace
Down to the detail:
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We define the “quantity of motion” as
the product of the mass and the
velocity.
momentum=mv
momentum is conserved
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it remains constant
Collisions
If energy is conserved,
the first ball will stop and
the second ball will move
out with the velocity
of the first.
TOTAL momentum is
therefore conserved for
a SYSTEM of particles.
A ball of air
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Pressure caused by
the collisions with
the wall of the
enclosure.
Motion of the
molecules is
RANDOM.
Average velocity of
the gas molecules is
ZERO.
Pressure Wave
Higher pressure region,
higher density,
Average velocity to the
right.
Lower pressure region,
lower density,
Average velocity also to the
right.
A Wall
Oh, Oh, another wall!!!
Wall is a velocity node
but a
Pressure Anti-node
due to the wave itself.
Lots of collisions!
Average velocity at wall is zero
Wave is reflected
Open End
REFLECTION
The standing wave
Both Open and Closed Ends of
Tubes Produce a Reflection
Lips
Nodes, etc.
The entrance to the pipe is sealed from the atmosphere by
the player's lips, and the pressure can vary maximally as
the lips open and close: indeed, it is the large variation of
pressure in the mouthpiece that (usually) forces the lips to
vibrate at a resonance of the bore. So at this end we have
a pressure antinode.
Most of the time, the lips are closed so the lips represent a
velocity node.