[Top] [All Lists]

Re: DIY Parabolic Dishes.

Subject: Re: DIY Parabolic Dishes.
From: "Walter Knapp" waltknapp
Date: Sat Oct 7, 2006 1:58 pm (PDT)
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.


<Prev in Thread] Current Thread [Next in Thread>

The University of NSW School of Computer and Engineering takes no responsibility for the contents of this archive. It is purely a compilation of material sent by many people to the naturerecordists mailing list. It has not been checked for accuracy nor its content verified in any way. If you wish to get material removed from the archive or have other queries about the archive e-mail Andrew Taylor at this address: andrewt@cse.unsw.EDU.AU