I thought at first of the membrane analysis, which of course involves
Bessel functions, and which has been fully analysed in the text
books. There is, however, surely a difference between a circular
membrane contrained at the edges (and even sometimes elsewhere) and
air, which consists of independent and unattached molecules, though
their motiion is constrained at the walls -- and this is the only
thin in common with the molecules in a membrane. Membrane behaviour
must be different. The vibrations of the air that get reflected from
the walls are not up and down, as in the membrane motion, but in
horizontal directions. I continue to expect that there is an
"infinite" number of modes, all at the same frequencies, due to the
diameter being the same in all directions on the horizontal plane --
assuming we have a perfectly cylindrical room.
I visualize this by starting with the four walls or a square
room. There will be two similar horizontal sets of modes at the same
frequencies. Now make it octagonal and there are four sets of modes
at the same frequencies. Keep doing this and in the limit you arrive
at a circular wall with an "infinite" number of modes... Of course,
there is some friction, but the effect would surely still be to have
greater response at certain frequencies and not much in between them.
I would look to see if any work has been done on the behaviour of
comparable frequency transveres radio waves in circular waveguide.
David
At 12:48 06-03-16, Augustine Leudar wrote:
>Im actually working on a sound installation which is involved with acoustic
>archeology in which Im hoping to experiments with resonances , this kind of
>thing :
>
>http://www.otsf.org/archaeoacoustics.html
>
>In this case a huge circular henge (3.5 m high banks) 180 m in diameter.
>
>https://en.wikipedia.org/wiki/Giant%27s_Ring
>
>Obviously with no roof resonance will not be as pronounced but there is
>still likely to be some sort of modal behaviour, especially if there had
>been many people singing/chanting etc . Apparently you cant work out modes
>for circular structures in the normal way by halving wavelength in relation
>to room dimensions etc A family member of mine is a physicist and
>suggested this might be useful to work out modes for an open circular
>structure :
>
>https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane#Animat
>ions_of_several_vibration_modes
>
>
>
>Then the following equation :
>
>Lowest frequency will be from longest wavelength which is 2 X pi X r/2.404
>(where r is radius of your circle) the next frequency has wavelength 2 pi
>r/3.83 = 1.64 x radius. And then 2 pi r/5.135 etc etc
>
>However this gives very long wavelengths - the highest mode is 11.61 there,
>but for me to calculate audible modes I would need numbers in this series
>above 150 or so (to get shorter audible wavelengths.
>Could anyone give numbers in the same series of numbers but above 150 ?
>
>
>
>
>
>
>
>
>On 5 March 2016 at 21:31, Martin Leese <martin.le...@stanfordalumni.org>
>wrote:
>
>> Augustine Leudar wrote:
>>
>> > Ive had a search online but cant really find much literature about this.
>> > Can anyone tell me anything about the acoustics of circular rooms/spaces
>> ?
>> > How to standing waves behave in circular spaces ?
>>
>> There was a discussion several years ago in
>> one of the rec.audio.* newsgroups on standing
>> waves in *spherical* rooms. Unfortunately,
>> Google Groups has deleted all the older posts,
>> but this post might be it:
>> https://groups.google.com/forum/#!search/"spherical$20room"$20audio/
>> rec.audio.pro/hLCCrmlSFdw/Lq_80PhAZQ0J
>>
>> (In case the link does not work, I went to
>> groups.google.com and searched for:
>> "spherical room" audio
>> with the double quotes.)
>>
>> Regards,
>> Martin
>> --
>> Martin J Leese
>> E-mail: martin.leese stanfordalumni.org
>> Web: http://members.tripod.com/martin_leese/
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>
>
>
>--
>www.augustineleudar.com
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