Standing waves in spherical loudspeaker enclosures
Brian O'Neill
Top Secret and Olson, Muller, Black and Dunn were not allowed to publish
anything involving advanced acoustic research. Acoustic weapons using WWII
technology, particularly infrabass, are problematic and so they were never
deployed on the battlefield.
After the war was over, it was declassified and Olson was allowed to
research and publish in 1950.
In the 60's, a company called Soundsphere was founded by James Westlund and
proceeded to take advantage of the unparalleled(pun intented) clarity and
dispersion offered by spherical enclosures. Thousands installed worlwide,
Indy 500, Winternationals racetrack right here in Pomona, World Ice in New
York City, PA system in a Ford factory in Detroit, etc, etc, etc.
The National Science Foundation conducted experiments in the 1970's and
80's to do psychoacoustic research using a computer-controlled 3-D array of
spherical speakers.
And of course in the 90's Cabasse in France, Gallo in New York, and yours
truly kept carrying the torch into the home and home theater venues.
There are no problems with standing waves in our current enclosures. The
only possible standing wave problem that would EVER arise with a spherical
enclosure would happen, first, if teh enclsorue were empty, with no
stuffing.
It would ONLY occur when the interior diameter becomes equal to one half of
teh wavelength. Please note that this is only ONE wavelength. This
so-called "problem" is easily solved by simply placing some stuffing at the
center of the sphere. Furthermore, we have eliminated this problem for
wide-range and midrange drivers(where the diameter may actually become equal
to 1/2 the wavelength) by building an egg-shaped (ovoid) subenclosure into
our spheres. Resonance (standing waves) is a function of power, frequency,
and three properties resistance, mass, and capacity. These three properties
may be mechanical, acoustic, or electrical.
-kris
Art Ludwig
Brian O'Neill wrote in message ...
> There are no problems with standing waves in our current enclosures.
The
>only possible standing wave problem that would EVER arise with a spherical
>enclosure would happen, first, if teh enclsorue were empty, with no
>stuffing.
> It would ONLY occur when the interior diameter becomes equal to one half
of
>teh wavelength. Please note that this is only ONE wavelength. This
>so-called "problem" is easily solved by simply placing some stuffing at the
>center of the sphere. Furthermore, we have eliminated this problem for
>wide-range and midrange drivers(where the diameter may actually become
equal
>to 1/2 the wavelength) by building an egg-shaped (ovoid) subenclosure into
>our spheres. Resonance (standing waves) is a function of power, frequency,
>and three properties resistance, mass, and capacity. These three
properties
There are an infinite number of standing wave resonant frequencies in a
spherical cavity. These solutions have been well known for decades. The
resonant frequencies are obtained from the roots of spherical Bessel
functions, found for example in the NBS Handbook of Mathematical Functions.
The first resonance occurs when the diameter equals .371 wavelengths, not
.5. The next two resonances are at .783, and 1.156 wavelengths. As
frequency increases, the number of resonances increase without limit. If the
walls are rigid, and the cavity empty, the resonant frequencies have nothing
to do with power, mass, or resistance. They are strictly a function of the
diameter. It is true that internal resonances are easily controlled by
stuffing the enclosure. This is equally true for rectangular boxes.
The enclosure walls also have resonances, which do depend on mass, and are
completely different from internal standing waves. It seems quite likely
that spheres have less of a problem with wall vibrations. At low
frequencies the only possible vibration mode is a variation in the diameter,
and it would be expected that this would produce much less movement than for
a box. However at higher frequencies spherical shells have complex
vibration modes thay may not be that much stronger than a box.
It is also true that in general spheres have less of a problem with
diffraction than a free-standing box.
Regards, Art Ludwig, www.thesoundpage.com