[sdiy] solid geometry

[Czech Martin]

Hi John,

I'm about to do the same, basically.

Aside from those geometric questions there is another
thing: an array of speakers will tend to "beaming"
if wavelength is reduced, rule of thumb: lambda <= distance.
That is: even if you make a large effort to create a
very good sphere and many speakers, there is a frequency
where this thing will not act as spherical source (this is
what I think you're after) but as bunch of sound clubs.
At least if the individual speakers are larger then 3cm diameter
or so. An average chassis might have 10cm diameter, so beaming
will get an issue around 3000 Hz already. About three octaves 
to come.
OTOH, at low frequencies also a cubic box will be a perfect
spherical radiator. You can now try and form the beams, but
I think you can never get rid of them.

What I planed was: use a car stereo full range (two system coax)
speaker in a cube. One speaker. Point it to several directions.
Overlay the different impulse responses. If linearity is observed,
this is similar to having the same amount of speakers.

Since linearity is crucial for recovering the impulse response
(nonlinearities will mess up the deconvolution),
it is a good idea to have more speakers, thus reducing the
individual amplitude. After all, speakers are very nonlinear.
I still have to do some work, here. What level of harmonics
will be tolerable? I do not know so far.

So perhaps I get another 5 car coax speakers and build a 
6 speaker cube. Mounting point at some corner.

There are other questions: You need to have the anechoic response
of your radiator/microphone/preamp/amp system
in order to obtain the true impulse response.
Otherwise the impulse response will be coloured by (mostly) speaker
imperfections (I'm talking about linear distortions).
I.e.: droop in bass and treble, phase "bending", partial resonances,
enclosure resonances.
Now, if you have a multi speaker system, the anechoic impulse
response will depend on microphone/speaker position a lot more
then it does already with a conventional system. The clubs.
So what sample do you take as "the speaker impulse response"?
The average?

I don't own an anechoic measurement room. Recently I came across
half space measurements. A large parking site could serve
on Sundays. I.e. a plane with (ideally) no buildings around.
So you will only have ground reflections. Still those have a dramatic
effect. If you think about a point source, the reflections can be modeled
with a mirror source. Depending on height about ground and microphone
position there will be a lot of peaks and notches (+-40dB or so)
starting at some
frequency. With that in mind, all those discussion about a 0.5dB
ripple in an anechoic measurement become pointless.
Perhaps it is possible to damp these with foam rubber in the 
mirror area between speaker and mic.


If e.g. a trumpet has a certain direction in the church, it will
sound different than pointing into the opposite direction.
So maybe a beaming source has some advantage.

However, the diffuse sound field after some reflections should
not differ that much, even if the radiator has some beaming.
So all these difficulties should not stop you doing this.
Even my very simple experiments with the balloon explosion
some years ago had nice results, the characteristic of the
room was preserved, though some high frequencies seemed to miss.
The balloon had some high freq roll of, and each one was different.
An ideal impulse sounds like "Click", the balloons made "plaff".
If you listen to ideal impulses via good headphones and compare that
to your home listening speakers, there is certainly some difference.
The more if they are vented speakers. 

Anyway, I bought a car stereo 10W amplifier with step up switcher
but linear power stage. And a battery. Togehter with a portable
CD player plus DAT recorder this will make a completely independend
portable measurement set up. I only worry about the DAT.
It is not oversampling, i.e. it is sensitive to out of band components.

m.c.








> -----Original Message-----
> From: owner-synth-diy at dropmix.xs4all.nl
> [mailto:owner-synth-diy at dropmix.xs4all.nl]On Behalf Of John L Marshall
> Sent: Samstag, 3. Januar 2004 21:41
> To: synth-diy at dropmix.xs4all.nl
> Subject: [sdiy] solid geometry
> 
> 
> Math Gurus,
> 
> I am building a spherical speaker to obtain the impulse 
> response of acoustic
> spaces. I have a sphere with circumference of 38.25" and 25 
> speakers that I
> believe are suitable.
> 
> The speakers are 3.5" diameter (will surface mount in a 3.0" 
> hole)  with
> paper cone and rolled rubber surround. I measured the free 
> air resonance of
> one speaker to be 110 Hz. These ancient ears could hear sound from the
> speaker up to 15 kHz.
> 
> I want to mount the speakers evenly distributed on the 
> sphere. What is the
> formula for doing this?
> 
> I have found formulas for dodecahedrons and icosahedrons but 
> they describe
> 12 and 20 flat surface solids.
> 
> Math wizards help me out.
> 
> Happy New Year,
> 
> John
> 
>