Horns: Vibrations and resonances in metal horns

[Rocky]

I was discussing horns with a guy working at a local army workshop in possession of the neccesary milling equipment, and after looking at my preliminary drawings, he suggested metal as material of construction, in oppose to my initial approach to use wood.

From an asthetic point of view, I liked his idea of using metal very much.. Regarding choice of metal, I think messing is a good choice as it's more rigid and dense than the aluminium alternate. At this point I am not sure about the composition of the messing he will be using, but it is normally 70% copper(Cu) and 30% zink(Zn)

Where my mathematical headache starts is when trying to figure out how thick to make it to avoid resonances, and at how many cycles it will resonate at a given thickness?

The horns are 40cm diameter and with tractrix contour
Y=20*ln ((20+sqrt(20²-x²)) / x) - sqrt(20²-x²), have a length of 35,5cm and the driver mounting plate at the horn throat is 1cm thick, 13cm diameter, with the 5cm diameter throat end hole... plus four drilled screw holes to attach the driver..

The horns will not play any sound below 270 cycles, so I guess a resonance below this would be ideal.. if it can be done..

Any mathematic genius out there with an approach on how to calculate my desired horn thickness? Svante?


EDIT: here's a downscaled drawing:

[Rocky]

diyAudio.com doesn't seem to update my attachement, probably a bug or something.. here it is anywayz...

[John Sheerin]

FEA would be the easiest way to figure out what the resonant frequency would be (besides building one). Depending on how it resonated, exactly, it would possibly work better to have the fundamental resonance above the range you want to use it in, not below. So make it very stiff - ie, make very thick walls. I would just build it, making it as massive as possible, and then damp it if it has audible resonances. I'm not sure on your fabrication method, but if your friend will be turning it out of round stock using a lathe, for example, aluminum might be cheaper than brass... If you are turning it out of round stock, I would not make a thin wall like you have drawn - just leave all the extra material on the outside of the horn. The only reason I can think of to make a metal horn with a thin wall would be if you were spinning it, but that is usually done with very thin metal, and it would ring like crazy.

[Rocky]

While brass might be more expensive than aluminium, Al still has a mass index of 2,7 (10^3kg / m^3) versus Cu/Zn alloy with an mass of 8,96 on the Copper and 7,13 on the Zink.. I think I'll pay the extra bucks for this mass, and Cu/Zn alloy looks really great too.. The price is actually not bad at all, I got an estimate of just above $200 for materials and manufacturing of both horns (as shown attached to my 2nd post).

Now, I'm not quite sure about the fabrication method they will be using. The workshop manager is on vacation this week, so I'll send a quote request for a thicker alloy horn when he gets back, and check fabrication method, whether I can go REALLY thick or not..

Am I far off track if designing my horn with roughly the same weight as a good working wooden horn? Will my alloy horn have roughly the same resonance properties as the wooden horn with the same mass and inner contour?

BTW, Does anyone know the weight of 1 cubic meter of solid wood, say maple, MDF, ply, or something.. just to give me an idea..?

[till]

Will my alloy horn have roughly the same resonance properties as the wooden horn with the same mass and inner contour?

No. Completely different.

Does anyone know the weight of 1 cubic meter of solid wood, say maple, MDF, ply, or something.

Density of wood varys from ~ 0.13 (Balsa) to ~ 1,23 for some tropical woods, ebony.

spruce ~ 0,43

oak ~ 0,65

maple ~0,6

[Rocky]

Does different materials have different "resonant properties" in addition to mass and shape?

Does anyone have experience with making horns in metal? Most of the old WE horns were made of relatively thin aluminium sheets weren't they? By making the walls say 1cm thick, out of Cu/Zn alloy, am I likely to experience resonance problems?

[till]

Does different materials have different "resonant properties" in addition to mass and shape?

do you think a bell made from steel and one made from rubber do sound the same?

i suspect it is connected to the amount of energy stored in the material by deformation (spring) and the amount of energy turned into heat , damper. This charakeristic will influence how good the system does resonate.

Think about a cars spring and damper system. resonant frequencys are give by mass and spring constant, and is damped out with the dampers.


Not only the spring constant of piece of wood will be different than of metal, as E is different, also internal damping will be different as its a fibre material with internal friction.

[Rocky]

Originally posted by till
do you think a bell made from steel and one made from rubber do sound the same?

Definitly not

Originally posted by till
i suspect it is connected to the amount of energy stored in the material by deformation (spring) and the amount of energy turned into heat , damper. This charakeristic will influence how good the system does resonate.

Think about a cars spring and damper system. resonant frequencys are give by mass and spring constant, and is damped out with the dampers.

Not only the spring constant of piece of wood will be different than of metal, as E is different, also internal damping will be different as its a fibre material with internal friction.

So since most metals have excellent resonant properties, is it in generic a bad idea to use metal for horns? Should I go for plastic or wood instead, making just the throat adapter in metal?

[till]

So since most metals have excellent resonant properties, is it in generic a bad idea to use metal for horns? Should I go for plastic or wood instead, making just the throat adapter in metal?

who should answer this?

altec made pretty metal horns, and i wish i would find a pair of them for small enough money:
http://www.tap-co.com/511b.jpg

The only way to find out how it will sound is to build it.

i would definitely not use plastic.

[Rocky]

OK. Thanks Till. Think I'll just go forward with trial and error.. I'll be expensive errors though

I will have some days to decide how thick to make the walls, I'm not going to make it a massive cylinder even though it would probably be the best.. But I'll make sure to give them *some* mass... I'll report back on my error trial process