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Re: DIY Parabolic Dishes.

Subject: Re: DIY Parabolic Dishes.
From: "Walter Knapp" waltknapp
Date: Mon Oct 9, 2006 3:30 pm (PDT)
Posted by: "Randolph S. Little"

> Yes, think about it some more.  The microphone is immersed in the 
> acoustic medium (air), such that a passing acoustic pressure wave 
> effectively wraps completely around it almost as if the microphone 
> were not there.  One of the great challenges of microphone design is 
> to make that "almost" as complete as possible across the entire 
> spectrum of interest.  This is especially difficult at wavelengths 
> short compared to microphone dimensions, and various types of side- 
> and rear-porting are typically used to flatten performance as a 
> function of direction and wavelength.

Indeed, mic design is not a simple thing.

Yes I more or less agree with your description here of a acoustic 
pressure wave interacting with a microphone. It is part of what I've 
been pointing out that argues against partial interaction of the wave 
and the diaphragm.
> This discussion pertains to pressure gradient microphones, which are 
> typically what we all use in the field.  (I apologize to any users of 
> velocity mikes who may feel left out.)  The small volume of air 
> trapped between the diaphragm and the backplate rests at ambient 
> static pressure.  As an acoustic wave surrounds the mike, the 
> instantaneous pressure on the exposed side of the diaphragm 
> oscillates around this static pressure at the frequencies of the 
> sound and at amplitude proportional to the loudness of the sound.  
> The diaphragm is faced momentarily with unequal pressure on its two 
> sides and, being compliant, moves in or out to compress or expand the 
> air volume behind the diaphragm to equalize the instantaneous 
> pressure.  This induced motion of the diaphragm, of course, is what 
> the microphone transduces to an electrical analog of the acoustic 
> pressure.

So far, so good.

> At all wavelengths much longer than the diaphragm's diameter, 
> regardless of direction of travel, the entire diaphragm 
> effectively "feels" the same oscillations of acoustic pressure, and 
> certainly moves in unison.  No problem.  However, at wavelengths 
> short compared to the diaphragm diameter, any off-axis excitation 
> will sweep across the diaphragm, rather than driving it all at once.  
> The exact response is dependent on the mike's porting, the lateral 
> compliance of its diaphragm, and probably many other arcane effects.

You have a little problem here. Think back about that planar sound wave 
arriving at the parabolic dish. Take the case of the sound from on axis 
and assume it's a 1:1 dish just to take a simplified case. And just for 
kicks the diaphragm is pointing in and not obstructed (no exotic mic 
design problems).

That wave interacts with all the surface of the dish and then arrives 
from all points of the dish simultaneously at the mic diaphragm (at 
increased amplitude compared to the wave as it entered the dish, the 
gain). It's not a wave from some specific direction for the mic, for all 
frequencies it's a integrated pressure wave arriving from half a sphere 
of directions (in the case we choose above). Now try and sweep that 
across the diaphragm at a angle, not the way it's going to happen. That 
is where I have a lot of problem with your explanation, particularly 
when you go back up to your first paragraph about how the pressure wave 
interacts with the mic.

> Actual measurements confirm the leveling-off of gain in the 
> neighborhood of 10 KHz for most of our reflector systems.  
> Mathematical "proof" of cause is elusive - not because we can't 
> calculate the acoustic performance of a parabolic reflector or of a 
> particular microphone, but because we must model BOTH elements at 
> once.  That's a real challenge!

At 10 KHz you have a wavelength of 1.2" or so. Much bigger than most 
diaphragms used, particularly bigger than those used in the Telinga. 
Though there you have to deal with multiple capsules. I've used single 
tie tac mics which are much smaller too. Are there actual measurements 
where diaphragm size is correlated with the falloff? Preferably with 
some reasonable statistical confidence level?

I'm not saying there is no falloff. I've seen enough graphs that it 
would appear there generally is a falloff in gain increase. I'm finding 
it hard to buy the explanation. The graphs I've seen of gain falloff 
also don't look like a singular cause for them.

Modern computers should be up to the task. I think the primary problem 
is that few are interested enough in the performance of parabolic mics. 
Probably no money for the effort.


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