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[Sven Friedrich]

G'day,

I'm stuck with the following: Please imagine a straight column array of N horn sub woofers. To maintain the mutual coupling between the elements, cabinets are to be placed as close as possible to each other. In a next step, delay shading is to be utilised to widen the directivity.

Now my question: the application of delay shading causes the complex pressure at adjacent hornmouth's to be no longer of the same phase. Each individual hornmouths' acoustic impedance remains unaltered by the applied delay - but which impact is to be expected in regards to the mutual coupling? I'm sure a thorough explanation would bust this thread, but some hints on available literature would be extremely helpful.

Kind Regards, Sven

[Tom Danley]

Hi

You dealing with things which have wavelength considerations attached, which makes most answers have the word “depends” in them.
If you have two subwoofer that are less than about ¼ wavelength apart, then you get the full benefit of mutual coupling which raises efficiency.
This condition (sources one quarter wl or less apart) is too small acoustically to have directivity.
If you raised the frequency or added boxes so that they woofers are about 1 wave length apart, then you have little mutual coupling but you have confined the radiation to around a 90 degree angle by virtue of its physical / acoustical size..
An array of subwoofers that was say 3 wavelengths across from side to side, in a straight row will have significant directivity however, the directivity is a function of acoustic length and so one finds the frequency response (not just SPL) changes with distance.

Placing the cabinets in a physical arc causes the radiated wave to behave more like it came from a  point source and so in the process of widening the dispersion, by making the dispersion change less with frequency also makes the response change less with position (distance).
That arc can also be created with time delays so that one can leave the cabinets in a straight line. Here, the center box receives an un-delayed signal and the ones to each side get a slightly delayed version and so on.  If you drew an overhead scale drawing of your system, you can try this by drawing an arc of say 90 degrees wide with the edges touching the outer boxes.  Now measure how far the center box is from that arc and note the value.  Now measure the different (closer) distance the box to the side is and find the “difference” value which is the delay that box needs. That delay is converted from distance to time via the speed of sound (about 1130 feet per second).
For each outer box, find that difference value and set that time delay.

You can get a feel for this quickly in a wave tank simulator (a great site). It is one dimension but shows what happens.
Lower the frequency, set up four sources.
Try this; set up an array of “close” sources in an arc vs straight, keep an eye on wavelength as all of this is wavelength dependent.

http://www.falstad.com/ripple/

Best,
Tom Danley

If you have LOTS of sources, then make the outer one say -10, the next one -6dB relative to the others.
If your interested, look for info on antenna arrays, arrays of dipole antennas and shaded amplitude arrays of antenna's.

I have been fiddling with a horn speaker who's amplitude is shaded vs angle, its weird stuff.
Bottom line, by the time an uni phase array is large enough to have directivty, it is normally too large to have much mutual coupling.