Klas and NatureRecordists,
Sten's article would be a good post for this group. The math may be too
complex to interest many, but the results should be widely appreciated.
In advance I'd like to caution readers about one practical aspect of our
parabolic reflector microphone systems that is omitted from Sten's
analysis; that is the finite size of the microphone's diaphragm. Sten's
analysis calculates the acoustic pressure at a point (the focal point) as
a function of frequency, and shows that the pressure at that point
theoretically increases monotonically with frequency.
Years ago Sten and I exchanged correspondence on this, as he had
cited similar work that I had published in 1963. My analysis yielded a
Bessel function equation which was too complex for solution by any
ordinary means at that time, and I left it for potential super-computer
solution. However, I was able to graphically illustrate the qualitative
shape of gain-vs.-frequency, and backed that up with quantitative
measurements on two different parabolic reflector systems.
The bottom line is: Bessel function behavior describes a series of
peaks and valleys in gain as frequency increases, each successive
valley becoming smaller as frequency rises.
Add to this the finite size of the microphone diaphragm, and gain will
flatten off above frequencies wherein the wavelength is less than the
diameter of the diaphragm. It is this significant practical aspect of the
overall system gain that Sten's analysis neglects. We both agreed
that a refined mathematical analysis that included the microphone's
effect would be nice, but more complex than either of us was willing
to tackle at the time.
Good recording,
Randy
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