What the heck is a node, anyway

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What the heck is a node, anyway?????

• September 26, 2005

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So far we have discussed

• A little music physics
• Tones
• Waves
• Frequencies
• Wavelengths
• Standing Waves
• Some musical Instruments

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BUT .

• We really havent much discussed

SOUND !
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We HAVE mentioned that

• Sound travels through the air.
• Sound is a pressure wave.
• 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.

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Speed of sound is affected by

• Temperature
• Humidity (Very Slight)
• Density of the gas (air)

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Temperature (Check my Arithmetic, please)

• 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 f440, this is about ½ Hz.
• A bigger temperature change would be noticed by a
  trained musician.
• Larger temperature excursions are possible.

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Gas

• 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.

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An Impulse Pressure Wave
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Moving along
v
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Process Repeats Itself ..
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A Sound Wave is Born
Fork is compressing the gas
Fork is expanding the gas
SOUND
etc.
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Oh where, oh where has my sound wave gone
Here? To be continued.
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It eventually gets someplace
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Down to the detail

• We define the quantity of motion as the product
  of the mass and the velocity.
• momentummv
• momentum is conserved
• it remains constant

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Mini-demo
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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.
momentum
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A ball of air

• 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.

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Pressure Wave
Lower pressure region, lower density, Average
velocity also to the right.
Higher pressure region, higher density, Average
velocity to the right.
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A Wall
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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
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Open End
REFLECTION
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The standing wave
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Both Open and Closed Ends of Tubes Produce a
Reflection
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Lips
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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.