Acoustics: Convert volume of a cube to an equal volume size right triangle container.

[csborgman]

I'm a musician building DIY sound absorption "panels" to help control low-frequency reverberation in my small, square studio. This is my first post. Did I do it right? LOL

I don't know the name of a right triangle that has volume, depth, or height. Please correct me if my thinking is wrong, a cube is a square with volume. If that's true, then what's the name of a right angle with volume?

OK, my problem. Convert the interior volume of a cube's known dimensions to produce an equal volume-sized right-angled-shaped container.

Basis. Many years ago the BBC developed several different sound-absorbing "modules" that were initially used in all their radio broadcast rooms and their control rooms. Later they were implemented in their sound recording studios and mixing rooms. They tested and developed two types of modules, a porous wide-band absorber (fiberglass or stone wool insulation) for frequencies 200 Hz and above. And a narrow-band membrane absorber with peak absorption at 125 Hz. Ironically (maybe not) this is exactly the frequency giving me problems.

The membrane absorber must have a sealed airspace to work. This module is then tuned by cutting out holes in the front membrane that would equal a certain percentage of surface space, from 5% to 20%. Based on Helmholtz's design.

These BBC modules are 580 mm on the sides with a depth/height of 184 mm. For a small studio such as mine, and many other bedroom music producers, this would take up too much space because you need 2-4, at least. There are porous absorbers that are designed to fit snugly into the most offending area of a room, the corners, I've built one. But I'd like to build a right-angle membrane absorber but I want to at least start with, a container with equal volume to the BBC module.

And I don't know how to do the math.

BBC module: Volume = 580×580×184 = 61897600 millimeters3

These measurements, I'm assuming, are for the exterior dimensions. The build material is 10 mm plywood for the sides, 6 mm hardboard for the back and 3 mm for the front panel membrane

 

[The Highlander]

I'm a musician building DIY sound absorption "panels" to help control low-frequency reverberation in my small, square studio. This is my first post. Did I do it right? LOL

I don't know the name of a right triangle that has volume, depth, or height. Please correct me if my thinking is wrong, a cube is a square with volume. If that's true, then what's the name of a right angle with volume?

OK, my problem. Convert the interior volume of a cube's known dimensions to produce an equal volume-sized right-angled-shaped container.

I think the "shape" you want is a cone.

You should (via Google) have no bother finding information/advice/examples on how to calculate the volumes of cubes & cones.

PS: I would suggest that a cube might be better described as a square with height (squares, as plane figures, don't have a "volume") or, more accurately, a cube is a 3D 'solid' with all six of its faces being squares. (They can, of course, be hollow; just saying 'solid' to indicate that it is 3 dimensional.) You may think that's just semantics but folks can get very upset in Maths forums if imprecise terminology is used.

 

[Dr.Peterson]

I don't know the name of a right triangle that has volume, depth, or height. Please correct me if my thinking is wrong, a cube is a square with volume. If that's true, then what's the name of a right angle with volume?

There are porous absorbers that are designed to fit snugly into the most offending area of a room, the corners, I've built one. But I'd like to build a right-angle membrane absorber but I want to at least start with, a container with equal volume to the BBC module.

A picture of what you want would have helped.

I wonder if the shape you are talking about might be a right-angle pyramid (that is, a pyramid with three perpendicular faces), which constitutes one corner of a cube. Here is what I'm talking about (though it's not solid):



I can't think of a better name for this shape by which to search; I just remembered that corner reflectors often have this shape.

As a pyramid, its volume is 1/6 the volume of the cube with the same edges. That is, the volume of a pyramid is 1/3 Bh, where B is the area of the base, which in this case is 1/2 ab, where a and b would be the perpendicular edges; so the whole formula is 1/6 abc, where a, b, and c are the three perpendicular edges, and 1/6 s^3 when they are all equal to s.

I'll keep looking for a better name and a site about it, waiting for you to help us out with a picture of your own.

 

[The Highlander]

I wonder if the shape you are talking about might be a right-angle pyramid (that is, a pyramid with three perpendicular faces), which constitutes one corner of a cube. Here is what I'm talking about (though it's not solid):

It occurred to me too, after my post (#2, above), that a triangular base prism or pyramid might also 'fit' the OP's "definition" of his desired shape so I suspect you may well be on the right track here.
Oddly, however, when I search for "soundproofed" rooms many of the results show walls covered in what look like square pyramidal frustums (a handy shape description originally explained for us by @Steven G if I remember correctly )