Re: Re: Vibration, damping, and weight


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Posted by Rick Denney on August 17, 2001 at 14:58:39:

In Reply to: Re: Vibration, damping, and weight posted by Gerald J. on August 17, 2001 at 13:21:27:

This confuses me.

Brass is like all metals that I know of in solid form. The stiffness of brass is nearly constant no matter whether it is annealed or spring-hard. The term "work-hardening" is accurate but misleading--a more meaningful term is "work-strengthening."

Brass can range in strength from 48,000 psi when annealed to nearly 100,000 psi when hardened to "extra-spring" strength. But the stiffness (as defined by the modulus of elasticity--the relationship between stress and strain) is about 16 million psi either way. So, unless the brass fails in strength (that is, deforms permanently), it will flex just the same under a given stress when dead soft or dead hard. Therefore, its vibrational characteristics and response should not at all be related to its annealed or hardened state, unless it is yielding, in which case it will be falling apart directly. A soft brass spring behaves just like a hard brass spring until we flex it beyond its strength.

Lead has a different elasticity, but it, too, is relatively constant. Lead/tin solder has a stiffness less than a third of brass, and pure lead is only about an eighth as stiff as brass. Interestingly, nickel and steel are about equal in stiffness (though steel is stronger)--both are about twice the stiffness of brass. I would expect a nickel tuba to resonate and respond much differently than a brass tuba, assuming the nickel is solid and not just plated. But even lead is elastic until it yields, it just yields very easily. So even lead will not damp vibration if a big glob of it is attached to the horn, as long as that glob is thick enough so that it maintains its shape.

As long as I'm busting myths, I have to go after the bronze is heavier thing. Yes, bronze is a bit more dense than brass with a density of 0.318 pounds per cubic inch. But only a bit. Brass has a density of 0.308 pounds per cubic inch, meaning that a brass mouthpiece of exactly the same dimensions will weigh only a little over 3% less than a bronze mouthpiece. Sorry, Matt.

Red brass (80% copper and 20% zinc) has just about the same stiffness as regular 70-30 yellow brass, so I resist the notion that its own resonance can be appreciably different.

Yes, brass gains strength and brittleness with age, which is called age hardening. But it doesn't affect the resonance of it at all. It just makes it hard to poke out dents without annealing it first.

Can residual internal stresses affect resonance by preloading parts of the structure? If a horn is assembled under stress (or even if parts are worked and not annealed), some parts of the structure will be left fighting other parts. But even with residual stresses, the added load caused by vibration will create the same deflection as when the brass is unstressed, because the stiffness is constant up to the bending strength of the brass. (This is known as Hooke's Law.) If the residual stress is high enough, however, the horn may dent or fall apart easier because it takes less external stress to reach the strength.

I've heard all along about how the acoustic characteristics of an instrument can be changed by annealing, but I do not understand what the mechanism for that can be. I surely do wish someone would explain it to me.

Rick "thinking stiffness and mass are the only determinants in elastic resonance behavior" Denney


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