Using Half of a Dome for Whispering Gallery Effect?

[arm27]

I wanted to know what are the ways I can have someone speak normally and the other person in another section hear the sound? (there's no closed rooms but there are mirror partitions occasionally)
So one of the things I thought of was using the whispering gallery phenomenon. To save space and have some control of my design I was wondering if the effect would be valid if half a dome was used instead of a whole one.
I saw many plans like the one below saying that the sound reflects and can be heard by someone on opposite side of the perimeter. So if we are cut of the other half, would it work? As also on many sites I read that the sound isn't only being reflected by the sides of dome but also the top and reflecting multiple times is what's causing it to amplify so much.

 

[A.T.]

... would it work?

There is no binary answer to this. To quantify how well it would work for specific rooms, you would have to run some simulations.

 

[sophiecentaur]

would it work?

You may be starting too far along the path of understanding this; there are some basics to be dealt with first.
The curve of the chamber will act in a similar way to how two paraboloid reflectors work; the paths from speaker to ear (think of it as 'rays') are the same over a wide angle (that's what we mean by focus) and sounds in different directions from the speaker will all arrive at the same time. Another conic section that achieves this is an ellipsoid in which people can stand at the two foci and get the same effect.
I see no reason why half a gallery wouldn't work because you can use parts of a paraboloid as excellent reflectors for microwaves.

In the whispering gallery, the same thing will apply but getting it right is not easy. The 'drain pipe effect' is what you get when there is a range of path lengths between speaker and listener because of dispersion. One problem with acoustics is the very wide bandwidth involved (several octaves of audio) and radio systems tens to be much narrower band (fractionally).

 

[Baluncore]

As also on many sites I read that the sound isn't only being reflected by the sides of dome but also the top and reflecting multiple times is what's causing it to amplify so much.

The sound is not actually amplified, it is simply not attenuated so much by destructive interference.

The sound generated at one focal point radiates outwards. If many reflective paths to the second focal point have the same length and transit time, then the majority of the sound will arrive at the second focal point from many different directions, with the correct phase to sum constructively.

The multiple reflections must be for multiple ray paths, with each ray having only one or two reflections.

 

[jbriggs444]

Here is a video. Look at the effect about 25 seconds in when a wave is generated from a source at one focus of an ellipse and seen to reconverge at the other.

 

[arm27]

I see no reason why half a gallery wouldn't work because you can use parts of a paraboloid as excellent reflectors for microwaves.

Hey, thanks for the reply. This will help me a lot.
Also, to actually design such a dome, is there a particular angle to the ellipse that I'll have to maintain or will it work with any?
Also when you say conic section, does it mean having a flat top face? similar to the image below?

 

[arm27]

Here is a video. Look at the effect about 25 seconds in when a wave is generated from a source at one focus of an ellipse and seen to reconverge at the other.

Oh that's quite informative. Thanks a lot for the help.

 

[Baluncore]

Also when you say conic section, does it mean having a flat top face? similar to the image below?

You show the generation of an ellipse.
Sections cut from a cone can be parabolic, elliptical or hyperbolic. When those are rotated about an axis they give domes that are paraboloids, ellipsoids and hyperboloids.
There are pictures here; https://en.wikipedia.org/wiki/Conic_section#Definition

A paraboloid focusses rays parallel to the axis to a common focus.
An ellipsoid focusses rays from one focus to the other focus.

A whispering gallery requires the floor be the height of a person below the focal point.

 

[tech99]

These examples do not use a circular gallery.
I thought the effect was caused by surface wave propagation around the gallery. I remember at St Pauls in London having to place my ear very close to the wall.

 

[tech99]

I have also discovered a piece by Lord Rayleigh, where he notes that the whisper is not only heard opposite the source, and he ascribes the phenomenon to guiding action caused by the general curvature of the surface.
https://archive.org/stream/theorysound05raylgoog#page/n147/mode/2up
He notes that this causes sound energy to spread in only one plane, causing it to fall off with 1/distance rather than 1/distance squared, as in open air.

 

[Baluncore]

I agree that a surface guided wave follows a concave curved wall ,with a continuous boundary reflection that maintains the wavefront. While the diverging radiated wave is subjected to less attenuation than free space, once it has followed through 90° of a spherical dome the wave will begin to converge again to a maximum at 180°. Reflections from the floor will be important.

A double wall forms a waveguide that guides the energy more efficiently with 1/distance.

Hyperbolic horns use a similar method to guide energy between a point and an aperture. The internal surface of the horn is doubly curved, radially concave, axially convex. The horn axis forms one virtual wall of the horn waveguide.

A circular hall, flattened vertically to an elliptical section dome makes an oblate spheroid. There will then be a circle of focal points that form an approximate focus for sound from the diametric opposite focal point.

 

[arm27]

A circular hall, flattened vertically to an elliptical section dome makes an oblate spheroid. There will then be a circle of focal points that form an approximate focus for sound from the diametric opposite focal point.

So basically, even if the ellipsoid is cut in half from the longer side, sound will be heard most clearly at the other focal points of that geometry?

 

[rcgldr]

I've actually experienced this at a multi-plex theater with a 30+ foot diameter circular dome like ceiling over a bunch of tables in the lobby area. Despite the noise of the crowd of people at the tables talking, if two people are standing just under opposite outer edges of the dome, they can hear each other talk, even if talking at low volumes.

 

[sophiecentaur]

I had two 1.5m dishes on opposite walls of my lab for demonstrations. Very disconcerting to walk through one focus whilst some child was walking through the other. My idiot head of department made me take them down (because it wasn't Chemistry, I think). They also worked, of course, for ultrasound and microwave experiments and were very up market .

 

[sophiecentaur]

So basically, even if the ellipsoid is cut in half from the longer side, sound will be heard most clearly at the other focal points of that geometry?

To get the effect you need the appropriate bits removed. This is unlike paraboloids which will work after a fashion whichever bits of each end are missing. For an ellipsoid, if the remaining bits are on the same side of the major axis, it will work. Just look at the diagram and see where the 'rays' go. Paraboloids work well at large distances of course.

image from Hyperphysics website.

 

[arm27]

Just look at the diagram and see where the 'rays' go.

Ohh Alright.
Thanks a lot my doubts are now clear.
I'll be able to plan for my structure now