Min Phase Horn with Faital Drivers at German DIY Show in Gelsenkirchen

[catapult]

Originally Posted by mige0

Always thought this is due to *absorption* effects ?

In the electrical/mechanical model, the absorption effects are caused by the lowpass filter.

Wow, started to get familiar with Austrian Ludwig Eduard Boltzmann (1844-1906) by reading his curriculum vitae last night and got impressed on a how widely interdisciplinary range this famous guy actually has been working.
Boltzman constant and Stefan-Boltzmann law being only the tip of the iceberg.

Ludwig Boltzmann – Wikipedia
Ludwig Boltzmann - Wikipedia, the free encyclopedia

Haven't arrived at what his theories may explain in the context of "speed of sound" though.

The Boltzman constant for a gas replaces the spring constant in the mass-spring model.

So – maybe a question beforehand – that from a mass spring chain some low pass filter and subsequent group delay occurs is clear (thend having outlined as well) but what's actually the trick that allows to flip from "group delay" to a "real delay" to establish "time of flight".

Group delay IS a real delay for a lowpass filter at low frequencies and goes to zero at high frequencies.

We've really gone beyond where the mass-spring model is useful but let's stick with it for a moment. The pics show the frequency response and group delay of 1 ball (blue) and 4 balls (red) with a resonance frequency of 10 KHz. Notice how the F3 moves lower and the group delay (real delay) grows larger at low frequency as you add more balls and a longer spring.

If you could build a molecular-size spring-balls gizmo, it might have an F3 for each ball in the GHz range. If you make it very long, say millions of balls, the combined F3 will start to shift down into the audio range and the combined group (real) delay will increase to measurable levels.

[rcw]

At the time the atomic theory was still doubted by many and the only model of the atom was an ideal perfectly elastic indivisible sphere, first proposed by the Greeks thousands of years before.

I think it was first Boltzmann who pointed out that since they knew that oxygen and nitrogen were diatomic, a more suitable model for them would be a pair of such spheres connected by a rigid rod.

This would explain why the speed of sound obtained by Newton was in error, he had considered only single spheres with three degrees of freedom and a diatomic molecule would have five.

This also partially explains the effect of water vapour on the speed of sound, the water molecule would have six degrees of freedom, and the speed of sound would vary in accordance with the partial pressures of these three gasses.

Later Van der Vaals showed that molecules have a fractional surface charge that causes interactions other than plain momentum preserving perfect impulse collisions.

All of this is very interesting but not really relevant for audio since the model of connected elastic spheres en mass acting statistically as waves in a smooth medium is perfectly adequate.
rcw.

[jzagaja]

Ok. guys here's directivity plot, 5 deg step, microphone distance 2 meters, 2" midrange driver (STX DT-1300Ti).

[jzagaja]

Or smoothed 1/3 octave.

[mige0]

Thanks for your effort to present measurements of the 1m Gaussian MinPhase contour - very much appreciated, Jzagaja !
Have a link to the compression driver used : STX DT-1300Ti ?

Michael

[jzagaja]

STX DT-1300Ti is a driver prototype made for me by STX Soundstation, probably most affordable, high-quality on the market. Smaller brother is here:

D-800-Ti - Sklep internetowy

[jzagaja]

Comparison between JMLC 350Hz (60cm mouth) and Minphase.

[jzagaja]

And finally directivity sonogram normalized to axial response.

[mige0]

Where it all started from:

Geddes on Waveguides










Above is not exactly the same Gaussian MinPhase contour thats finally been realized and what we now got measurements for – but might give some background nevertheless


Thanx again, jzagaja - great work !

Michael

[jzagaja]

Updated measurements with a good microphone Bruel Kjaer 4149. Directivity 10 deg step, 1/12 oct. smoothing.