Posted by: "Randolph S. Little"
> Good question Walt, and a helpful reference website. It is indeed
> the longitudinal wave motion that is transduced by the microphone,
> and it is this wavelength to which I refer. In air at standard
> atmospheric pressure, temperature and humidity the velocity of these
> longitudinal sound pressure waves is about 1000 feet per second. The
> wavelength of a 1 KHz sound is about 1 foot, that of a 10 KHz sound
> about 0.1 foot, etc. Thus, it is in the upper octave of human
> hearing (10 to 20 KHz) that the wavelength of the longitudinal wave
> and the diameter of the microphone diaphragm are the same order of
> magnitude.
For your 1 foot example the beginning of a single wave cycle will hit
the parabolic, or the mic diaphragm or whatever 1/1000 sec before the
end of that cycle. That's one wavelength in longitudinal.
We should remember that its not really a physical wave like a ocean
wave, or a vibrating string, but a variation in pressure. A variation in
pressure that's cyclic.
> At all practical distances from the sound source, the sound wave is
> planar by the time it reaches the diaphragm, and the whole diaphragm
> moves longitudinally as a unit, not unlike any one of the dots in the
> referenced animation of a longitudinal wave. However, in the focal
> region of a parabolic reflector, many identical longitudinal waves
> are converging from many directions, having been reflected from
> different facets of the reflector. Most of these components are
> impinging obliquely on the diaphragm, and therefore tend to sweep
> across the diaphragm instead of impacting it all at once. At lower
> frequencies (longer wavelengths) these differences are negligible,
> but as the acoustic wavelength becomes shorter these differences
> result in less net axial movement of the diaphragm, hence less
> sensitivity.
The problem with this is that it's a pressure wave, and pressure in a
gas is by definition equal in all directions. Sound waves do spread,
though not at the rate of forward travel.
If your description were true think about how a omni mic picks up sound
from it's own shadow. If it could only pick up sound that impacted the
mic diaphragm directly due to a line of sight between source and
diaphragm it would not have a omni pattern. It picks up sound from
behind because pressure is equal in all directions.
The actual pressure wave at the parabolic's mic is a mixture of
reflected sound pressure from all parts of the dish at all frequencies.
And both on axis and off axis sound travel. This is going on
continuously so the mic sees a integrated pressure variation in the gas
from all sources, not discrete sources from discrete directions. Unless
one takes as discrete sources individual air molecules, and those do not
pass the diaphragm at all, but oscillate around a equilibrium position.
Some will "impact" the diaphragm imparting some of the sound energy to
the diaphragm. But they will do so as gas pressure, following those rules.
When a single cycle of the sound wave arrives at the dish from along the
axis it's a planar pressure wave, ie variations in gas pressure with a
front that can be considered flat. It will sweep into the dish and if we
follow the leading edge of a single cycle it's going to hit the outer
diameter of the dish surface first and already be on it's way to the
focus as the planar wave sweeps farther into the dish. The reflecting at
any instant will be a circular pattern around the circumference of the
dish at that depth. I believe the idea with a parabolic is that the path
length from dish opening to focus remains a constant so the leading edge
of the pressure wave from all parts of the dish arrive at the focus as
a pressure that's multiplied over the pressure of the original arriving
wave at the dish opening. That's what causes the gain, the gain is
increased pressure, a stronger wave cycle of pressure. Thinking of it as
waves from different parts of the dish is probably misleading a bit.
Different frequencies will be represented by the rapidity of the
pressure variation.
I'm thinking the solution to the gain falloff may be found in the energy
transfers involved. It takes energy to increase pressure but in a
perfect gas system this is a net zero over the whole wave cycle as the
decreasing part returns energy. What I'm thinking may be happening is
that the higher the frequency the more rapid the pressure changes
involved which may involve greater energy cycling. At some point the gas
becomes less than perfect in that some energy is being lost as heat as
the total sound energy goes up. In other words these losses account for
the falloff in gain or a major contributor. (note this may also apply to
the loss of high frequencies over low ones with distance) Just a thought.
It would be real interesting to see if the guy running the display site
would do a parabolic animation. Would help to clear it up to see the
particle behavior involved.
> This is another good point for discussion. It turns out that minor
> deviations from true parabolic curvature are not terribly important
> to the acoustic performance of the reflector. At very, very short
> wavelengths this becomes important (as for light or radio waves), but
> at our acoustic wavelengths a dent or dimple here and there is of no
> consequence.
Probably because the focus zone we work with, and assume is so large, at
least the diameter of the diaphragm. And that the pressure wave that
arrives at the focus is a integration of reflections from the entire
surface of the dish. Obviously this variation in the time of arrival
from a irregularity will be greater for shorter wavelengths in terms of
phase shift. So, while it may not matter much overall, it's probably a
frequency dependent difference in how much out of phase is introduced.
The more perfect your dish the cleaner the signal you will get even if
the differences are small.
Walt
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