Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Acoustic impedance



I'll take a stab at both questions posed here.

(1) Reflection at open end.

In the hypothetical wave on a string with a free end, when the wave gets to
the free end, the end has a whiplash action in which it travels farther than
it would if more string were present past that point. When this reaches its
limit and snaps back it pulls on the previous section of string more than
that section would have been pulled if the displaced section were being
restored to the equilibrium position by string on both sides of it. So this
initiates a reflected wave.

For a sound wave in a tube coming to an open end, the displacement has been
constrained and becomes less constrained. It can suddenly propagate in more
directions. As the air molecules displace under less constraint, they
displace more. When they come back to equilibrium they are coming back and
interacting with the previous molecules in a different way than the
interaction that occurred from neighbor to neighbor within the contraints of
the tube. That initiates a new wave (the reflection) back down the tube.

If this seems nebulous, just admit that the motions of the air molecules at
the end of the tube will be different than the motions of the molecules
within the tube. Then admit that when the displacments/motions of air
molecules in a region of space is different than the surrounding areas, that
means a wave will propagate into the surrounding areas from that region that
is different.

(2) For a trumpet.

Although the mouthpiece end of a trumpet may seem closed, it is open. Think
of it this way... the characteristic of an open end is a pressure node...
i.e. constant pressure. The lips are vibrating in the proper phase
relationship with the reflected wave to maintain a constant pressure at that
point. When pressure from the reflected wave is not available the lips open
and the pressure is maintained by the pressure in the players mouth. When
back pressure from the reflected wave is available, the lips close. So the
lips are essentially a pressure-regulator, opening and closing at the right
frequency to keep the pressure in the mouthpiece constant... hence a
pressure node... hence an open tube.

Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817