Homemade Exponential Horn Project

[Inigo]

Just a note regarding something you said at the very beginning of this post. The theory of sound diffusion in a space supports your affirmation in the following sense.
When a sound source is emitting in the open space, irradiates sound in a complete spherical diffusion. If the source is then placed in a sound opaque, infinite plane, it irradiates to half space. Then the illusion when you're receiving the sound is that the source were double size, double power. If you yet half the space to a quarter sphere, it doubles again, and so on.
So placing a horn in a room so that it is located in one of the ceiling corners with two walls, this divides the irradiation sphere by eight, so the illusion is that your horn has eight times its mouth area. Or what is equivalent in practical terms : you design a horn for a given cutoff frequency, and to materialize it, if you're placing it in such a corner, you later can divide by eight the designed cross section of the horn in all its length. Of course, the resulting reduced areas conform a design that is no more a pure exponential or tractrix or whatever curve you decided to use, for these expanding laws are not linear to the area. But the effect in sound power is the same. So your horn roughly will work as if the actual area was eight times larger...!!! Practically means that when you place the sound source in the corner of a room, against two walls and the floor, or the ceiling, the sound power receives is much greater, and the bass response is noticeably increased.
You can do the experiment at home with a small portable radio or your mobile phone playing music. You place it on a table, and listen. Then, without touching the volume, place it in a corner on the floor and two walls, the speaker facing you, or facing the corner. Move yourself away from the sound source, so your ears are sensibly at the axis (bisectrix line) of the corner and then compare the sound you hear!

[Ethan]

Inigo,

What you described does correspond quite closely to what I had gathered, which makes sense—although I haven’t been able to find how close the mouth needs to be to the corner for the effect to work; I presume it should be as close as possible to the back. My family has a modern speaker in one corner of the living room, and on some songs the bass can be overwhelming even at low volumes (and even when playing electronic transfers of Orthophonic records, which I thought were supposed to have less bass than a perfectly flat recording response would give); I tried measuring the frequency response with my computer a while ago, and found a rather sizeable peak at about 70 Hz, so perhaps the speaker was just designed for different placement. Other than that observation, I haven’t tried the experiment you describe, but it sounds interesting; I think I will sometime.

Using the halving space-halving mouth area method for a 100 Hz. horn, and assuming that the mouth diameter in open space needs to equal the lowest wavelength to be reproduced, I’m getting a mouth area of 1463.22 square inches (21.58” radius) in open space, 731.61 square inches (15.26” radius) against one wall, 365.80 square inches (10.79’ radius) in a wall-wall corner, and 182.90 square inches (7.63” radius) in a wall-wall-ceiling corner.

Interestingly, when I cut off the 100 Hz. curve at a 10.79” radius, the horn has almost a 22” diameter mouth and—I believe—can be folded to roughly the same shape and size as the Mark IX horn, based on a few measurements that I found. Does anyone happen to know what a typical Mark IX frequency response looks like?

[Curt A]

Cotton fabric and cotton card stock are not similar in their characteristics, so stretching isn't an issue. Card stock with cotton just has small fibers mixed in with the paper for durability, it is not woven and should act like normal paper.

[Ethan]

Cotton fabric and cotton card stock are not similar in their characteristics, so stretching isn't an issue. Card stock with cotton just has small fibers mixed in with the paper for durability, it is not woven and should act like normal paper.

Good to know!

I’ve been visiting relatives for the past few days and haven’t made much progress on the horn, but I did get a stash of paper bags that seem to work better than the others that I tried, so I may not need to buy more paper, at least until I start work on the next section. I tried hammering out the former again, with no luck, so I made a rough sketch of a curved wooden “ramrod” that fits through the throat of the horn without catching anywhere; if it fits as well in practice as it does on paper, it should be able to transmit the force from the mallet to the former more efficiently than the Lego version.

The horn seems quite sturdy even at about 1/16” thick; I’ve tried pounding on it with a mallet to try to loosen the former, and it doesn’t show any signs of damage (although it also doesn’t show any signs of letting go of the former…). Has anyone else made EMG-like horns with plastic-like glue and thin paper, to say how their strength compares to the original horns?

[Ethan]

The horn is now about ⅛” thick, so I tried extracting the former again, this time using the wooden ramrod, but still with no luck—I looked inside the throat with a mirror, and it looks as though the end of the rod was just crushing the foam. I was able to excavate some of the foam near the mouth and pull out a roughly two-inch disc, but it was rather time-consuming, so I’ll probably try dissolving the rest with D-limonene; as it’s already damaged, there isn’t much point saving it.

The next steps will be filling in the gap where the paper shrank away from the end of the former, installing the wood ring that allows the two halves of the horn to be joined, and then adding another ⅛” of paper over that—fortunately, the new paper bags seem a little thicker than what I was using, so it should go a little faster now.

The horn with part of the former removed and part still inside.

The inside of the horn--the black line on the extracted piece of the former marks how far the paper shrank; to fill the gap, I'll put the extracted piece back in, and apply paper mâchê over it. The inner layers of the horn were originally off-white, but the Vaseline soaked into them and made them translucent, so now the interior is only a little lighter than the exterior...Methinks perhaps I might as well start the mouth with the sturdier brown paper, and maybe do a decorative final layer over the whole thing.

[Curt A]

"Has anyone else made EMG-like horns with plastic-like glue and thin paper, to say how their strength compares to the original horns?"

What glue are you using for this project that you describe as "plastic-like"?

Maybe the glue is adhering to the styrofoam and Vaseline is not a good release agent? Just wondering, since not all glue adheres to styrofoam... This is only a thought, not based on real experience... What if you used a glue that doesn't adhere to styrofoam for the initial layers closest to the form and after it hardens use something else for the outer layers - after the form is removed? Just thinking out loud... what do I know?

[JohnM]

Perhaps dissolve the foam with methylene chloride paint stripper, or acetone?

[dzavracky]

I used kitchen cling wrap on my mold… it separated on the first try.

David

[Inigo]

And the plastic film doesn't adhere to the horn paper?

[Orchorsol]

I used kitchen cling wrap on my mold… it separated on the first try.

David

Very useful to know, many thanks. That's what I've been planning to use at some point in future when I remake the majority of a broken EMG Mk IX horn.