The Ghost wrote:

Does your prediction of 0.2% distortion apply to the situation of a
piston in a tube or a piston in an infinite baffle, or doesn't it
matter?

First, that prediction is incorrect (I realized this
morning.) I accidentally plugged the 2 cm in as velocity
rather than displacement when doing the calculation but .2%
is correct for a magnitude .01 m/sec LF velocity.

The correct figure for 40 Hz at 2.53 m/s (2 cm throw) and 2
kHz at .05 m/sec (approximately equal acceleration, as is
closer to the situation with a driver in a cabinet) is about
25.4% RMS IM distortion. I find this rather startling.

The sidebands around the 2 kHz signal are -15 dB, -36 dB,
-60 dB, -87 dB.

These figures would obtain in a tube were it possible to
generate LF displacements that large when so loaded, and
they would not be distance dependant.

This simple plane wave analysis says nothing at all about a
piston in a baffle or a cabinet. The assumption of constant
characteristic impedence that it makes is no longer the case
even at the piston/air interface. A correct analysis would
have to take into account the radiation impedence seen by
the piston. I'm not sure whether the effect would be more
or less than in a tube when that difference is accounted
for. That's what I should look at next but I've fallen far
enough behind in what I really should be doing that I must
defer that.

As far as dependancy on distance from a speaker in a baffle,
I now don't think there will be much, if any, but thats only
a SWAG based on thinking that the frequencies of the IM
terms are close enough to the fundamental that they will
propegate from the plane of the speaker pretty much the same
as the fundamental so that the distortion as a percent of
the fundamental should not change much with distance.

Yes, this is a complete reversal of my thinking. The trap I
fell into was the false belief that the flow velocity at a
plane and the particle velocity about that plane were the
same. Having finally thought my way out of that
misconception and seeing that in fact they aren't even
related linearly (in free space as well as near a driver), I
see that I was wrong in what I believed followed from it.

This brings me back to the reason I began trying to
understand this to begin with, the quantitative
determination of how signifigant the effect really is. It
now seems to be more signifigant than has been assumed, not
less. Whether or not that remains true for more realistic
speaker couplings is an open question.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein