Posted by: "Randolph S. Little"
> Sten's analysis is excellent on the theory of parabolic reflector
> gain. If the microphone were an infinitely small device located
> precisely at the reflector's focal point, his prediction would be
> accurate up to the point where nonlineraities of the acoustic medium
> (air here) take effect. But our microphones are not infinitely
> small; their diaphragms are typically in the range of one to several
> square centimeters. The size of the focal "point" diminishes
> monotonicly with frequency. When that size becomes less than the
> size of the microphone diaphragm, no further gain can be realized by
> the reflector-plus-microphone system because essentially all of the
> focussed energy is being captured by the microphone. Even though the
> acoustic pressure at the focal "point" may continue to rise with
> frequency, the average effective acoustic pressure affecting the
> diaphragm does not. Thus, as Klas points out, rolloff occurs,
> although I would call it leveling rather than rolloff.
> This leveling occurs when the acoustic wavelength approaches the
> microphone diaphragm diameter.
What wavelength are we talking about here? Transverse or longitudinal?
It sure sounds like you are using transverse wave patterns in your
predictions, not the longitudinal pressure waves that's going to fit
sound. I really have a hard time coming up with a way of visualizing
that variations in the longitudinal wavelength will change the focus size.
(For those that don't know what we are talking about, here's a nice set
of graphics that illustrate the difference:
Note there are links there that can take you to spherical longitudinal
wave patterns, probably even closer to the pattern of the sound waves
from a calling bird in one of those. Though at typical distances for
parabolic use that and straight longitudinal won't differ much as a
I understand what you are saying, but I'd really like to know how you
came up with it? (preferably in a non mathematic logical description)
I'd think the size of the focal point was related to a lot more. Like
how perfect a parabola you had, it's surface roughness and so on. And,
of course, I assume you are talking about a sound source that's exactly
on line with the central axis of the parabola. As soon as that sound
source is off axis, even slightly, the focus point shape changes or
shifts position. That's why it's better to think of the focus of a
parabolic as a zone rather than a point.
I agree, measurements on real parabolics do indicate a falloff of gain
increase from the Wahlstrom predictions with frequency, his own paper
has some graphs of those. I wonder if anyone has tested your theory that
it's the mic diaphragm size by actual measurement. The falloff is not
the sort of smooth thing that would be predicted by one factor in any case.
Of course mic choice does change your recording, each mic has it's own
coloration of the sound it picks up. And if you are trying for that
unobtainable goal of reproducing the sound exactly as the original sound
you will have to deal with that.