Natural Science Forum / Physics / Acoustics / February 2004

I'm trying to write an applet to make plots of input impedance
and frequency response for conical and exponential horns of various
sizes. The only reference I have is Harry F Olson's
commonly-available-in-bookstores book "Music, Physics and Engineering."
The equations he gives for throat impedance of pipes and conical horns
are working for me perfectly and generating nice plots that match the
book's. But the equation he gives for input impedance of
exponential horns (equation 4.59 in this book) seems to only be valid
for frequencies above the horn's cutoff point. I'm designing air horns,
not loudspeakers, so I care mostly about the region below the cutoff,
because I want to see the peaks for the first few points where the
reactance is zero. Equation 4.59 is giving me nothing up to the region
where f=fc, some "noise" around that point (dfor lack of a better term),
and then a good plot with correct resonant peaks for f>fc. I've checked
my math over and over, and I just can't get a result from harry's
equation (4.59) below the cutoff. I am using trig and exponential
functions that are all complex number friendly, and I don't think this
is the problem. It seems to me that there must be another solution for
f<fc that is not in this book I have.

So my real question is: Does Harry Olson's "Acoustical Engineering" or
Beranek's "Acoustics" have a complete set of solutions for the
exponential horn? Or, am I just doing the math wrong and 4.59 should be
giving me what I need?

-Adam
adam at(@) airraidsirens dot(.) com