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In Reply to: RE: One of the thougest question in acoustics posted by mdg on May 23, 2007 at 12:55:36
Hi
Radiation into free space requires the energy to “go” somewhere and not come back.
Normally that job is accomplished by the sound radiating away from the source, with the result being that the acoustic load looks resistive or dissipative.
As one looks closer, one see’s this radiation resistance appears as a constant value above some source size and is a variable number below some source size (acoustic size, physical size relative to the wavelength).
When a radiator is acoustically small, then the act of placing a second driver at a distance which permits coherent addition, results in the radiation efficiency going up by two.
Thus, one woofer VS two identical woofers, one finds that the double unit has twice the power capacity, allowing it to handle twice the power AND the radiation efficiency is doubled. Now, one finds the double unit is 3dB more efficient AND handles 3 dB more power, it is 4 times louder than one.
There is an observed practical limit to this increase at around 25% efficiency (about 106dB 1W 1M) and this also stops when the drivers are more than about ¼ wl center to center at the farthest point.
Now, in a Tapped horn, using a program like AKABAK, both sides are enclosed within the acoustic cavity so mutual radiation is not an issue here, pressure is modeled on both sides etc. Akabak is very good and I used it to model all of the Tapped horns including this “portable” Tapped horn
http://www.danleysoundlabs.com/images/Matterhorn%20Finished.jpg
The construction video of it is kind of funny.
http://www.danleysoundlabs.com/matterhorn.htm
Best,
Tom Danley
Hello Tom (and others)
Your Matterhorn is real cool stuf, first because it`s
a unique subwoofers and secondly (funny part) is that you
could keep your BBQ`s indoors.
Still something about your answer confuses me a little bit.
Suppose you have driver firing in a closed box, it`s sees a reactance according the compliance cq. volume.
Putting 2 drivers in that grounded enclosure, each driver is loaded with a increased reactance with a factor 2. This shows up in the excursion plot.
what confuses me is that you don`t see a chance in excursion when only one speaker is driven instead of two, other than the change in reactance.
To me it`s make sense, that one driver is putting a pressure on that second driver.
That excursion plot in your white paper, is that for a single Tapped Horn driven stand alone?
Cheers,
Marcel
Thanks, Tom.
I have a question.
Does the beginnings of cancellation set in when the drivers are 1/4 wavelength apart center-to-center, or outer-edge-to-outer-edge (assuming they're in the same plane)?
I recently built an experimental box using dual direct-radiator woofers, and the effect of cancellation on the power response was more severe than I'd expected. I'll either have to use woofers with an upward-sloping response or equalize or fuggedaboutit.
So, when ya gonna build a full-size version of that little portable tapped horn??
Cheers,
Duke
Hi DukeWhen sources occupy a space less than about ¼ wl in diameter, they add fully, coherently in all directions. Addition of phases goes by the cosine of the angle (difference between) and that is what is really going on.
Larger spaces are usable too, at 1/3 wl center to center, one develops a forward lobe, at 1/2 wl as in line sources, there is a null in line but a beam formed on axis.Basically, when the phase differences between the sources are small then addition is coherent, equal in all directions. As the spacing gets larger, preferred directions, lobes and cancellation nulls are produced where addition and cancellation is complete
Hey, since I can post pictures now with the new format (thanks btw Rod and the Bored one), here is a graphic which shows a “stack” of radiation patterns for a pair of sources, operating from 0Hz to a high frequency where the spacing is about 6 ¼ wavelengths apart.
You can see it goes from a round pattern when the addition is coherent to a more complicated spider as the acoustic spacing increases.On your woofer, if the drivers are less than about ¼ wl apart at the highest frequency used, then they will not traverse a change in operation.
Did you have chance to measure them outside to see what they do on there own?
If the drivers are acoustically “far apart”, maybe you can taper one off as the frequency climbs?Yeah, full size, I suppose when someone is willing to write the check haha.
Seriously, even this one might be fun at a football game or something.Best,
Tom
I still like “Dukes song”
Sue the guard up at the lake, there’s sawdust and Pizza Yoda
http://www.youtube.com/watch?v=_fSpI4oZoDc&mode=related&search=
Thanks for the picture, Tom! Very enlightening.
I didn't take outdoor measurements; only nearfield on-axis and off-axis time-gated, and farfield off-axis non-gated (the latter to give me an idea of what's happening with the power response).
Duke
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