1. What the heck is a node, anyway?????
September 2006

2. So far we have discussed
A little music physics
Tones
Waves
Frequencies
Wavelengths
Standing Waves
Some musical Instruments

3. BUT ….
We really haven’t much discussed
SOUND !

4. 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.

5. Speed of sound is affected by
Temperature
Humidity (Very Slight)
Density of the gas (air)

6. 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 ~ For f=440, this is about ½ Hz.
A bigger temperature change would be noticed by a trained musician.
Larger temperature excursions are possible.

7. 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.

8. An Impulse Pressure Wave

9. Moving along ~v

10. Process Repeats Itself …..

11. A Sound Wave is Born etc. SOUND Fork is compressing the gas
Fork is expanding the gas
SOUND
etc.

12. Oh where, oh where has my sound wave gone …
To be continued.

13. It eventually gets someplace

14. Down to the detail:
We define the “quantity of motion” as the product of the mass and the velocity.
momentum=mv
momentum is conserved
it remains constant

15. Mini-demo

16. 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

17. 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.

18. Pressure Wave Higher pressure region, Lower pressure region,
higher density,
Average velocity to the
right.
Lower pressure region,
lower density,
Average velocity also to the
right.

19. A Wall

20. Average velocity at wall is zero
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

21. Open End
REFLECTION

22. The standing wave

23. Both Open and Closed Ends of Tubes Produce a Reflection

24. 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.