Re: Acoustic impedance

[Bernard Cleyet <anngeorg@PACBELL.NET>]

Here's an answer from an Astro Physicist friend:

bc   (I think he misread part of your question (remember, a quick answer)

OK -- here are some quick answers.

Bill

> Bill!
>
> Do you have a reference or quick explanation for this guy?
>
> Tanks,
>
> bc
>
> P.s. Pse. put me on your list for Funk concerts, etc.
>
> Jeff Marx wrote:
>
> > Here's something that' been bugging me and I hope that someone on this
list
> > will be able to help me out...
> >
> > Imagine a sound wave traveling inside a tube (treat it as a plane wave).
> > When the wave reaches an open end of the tube, part of the wave propagates

> > into the the room and part of the wave reflects back into the pipe. One
> > simple way to explain this phenomena is to cite that the acoustic
impedance
> > changed at the opening. (Acoustic impedance, Z, of a pipe is given by Z =
> > pv/A, where p is the density of air, v is the speed of sound, and A is the

> > cross-sectional area of the pipe) When the wave reaches a boundary with a
> > different impedance it generally is partially reflected at that boundary.
> > This is all fine and dandy; however, I'm looking for a more physical
> > argument, one based on what is going on with the air molecules (or better
> > yet, small packets of air). How does the longitudinal wave "know" when it
> > has reached the end of the tube. I feel that a full explanation would
> > describe the diffraction of the wave at the tube opening, as well. But
> > perhaps this is reaching too far.

When the compression pulse emerges from the end of the tube, it is able
to expand in all directions. When it expands, however, the expansion does
not stop at the equilibrium atmospheric pressure, but continues further,
carried by inertia. At that instant there is a relative underpressure
(rarefaction) just outside the end of the tube, and air in the tube rushes
out to fill the partial vacuum. This causes a rarefaction wave to move
back along the tube.

> > All of this leads to answering a, perhaps, more interesting question: "Why

> > does a trumpet, which seems like a closed pipe, produce a nearly harmonic
> > set of overtones, without any missing harmonics?" The hip-shot response is

> > because it has a bell (and a mouthpiece), which changes the "effective
> > length" of the instrument for different frequencies. I'd like to
understand
> > this better.

The trumpet produces many harmonics because it is being driven by a periodic
(non-sinusoidal) lip vibration which has a power spectrum consisting of
many harmonics; many of these harmonics can drive resonant modes of the air
column.

> > I've gone through the mathematical derivation in Rossing's book "The
> > Physics of Musical Instruments" (a text I highly recommend) and it's quite

> > straightforward, but it doesn't seem to provide me with a lot of physical
> > insight - which is unusual for Rossing.

Fletcher is the guy, not Rossing!

> > Thanks in advance,
> >                         Jeff