Thread: Acoustic Resonance

Hey! I was just wondering if someone could enlighten me about acoustic frequencies. I'm writing a story and would like to know if iron or steel [swords] have resonant frequencies... and in addition, if they do, how much they would vibrate [and what affects how much they vibrate?]. thanks!

From the little I know then...

If you push something it will move. If it is unconstrained it just carries on moving. What normally constrains the things around us (stops them just moving for ever) is friction. A piece of steel would, if you pushed it, just move away from you and like everything else eventually stop moving because of friction. If however you held the piece of steel it, say at one end, and pushed it, say at the other, it would not move away but the free end would instead move forward and backward. Just as with free movement the steel would not keep going forward and backward forever. Friction with the air and internal friction would convert the energy of movement into heat and so the steel would come to a stop. A very, very small amount of energy would also pass into the air as pressure waves. If the steel was moving at the right frequency these would be within human hearing and qualify as sound waves. The repetitive movement would occur at the resonant frequency of the system meaning the piece of steel plus how it was being held. What determines how well the steel resonates include:

o The shape of the steel
o How it is being held
o Its internal friction

What stops the steel resonating, as I said, is loss of energy. This is known as damping. Damping can come from outside like the air around the object or from inside. Rubber is highly damped and burns up a lot of the shape-changing movement as heat energy. Steel is less damped so it makes for a better resonator. But it is not just the material that matters - the shape is also vital. Longer thinner shapes make better resonators. To be useful for creating soumnd waves though you do need to lose some energy. You need to send some out from the object as sound waves. Hence the tuning fork is a great example of a long thin steel shape optimised for minimum damping and maximum transmission of sound. I believe, but to be honest I do not know for sure, that iron is more damped with internal friction than steel. However all steels are not the same and so some will be better resonators than others.

So in answer to your question you need:
o a material that is not very self-damping (which does not turn a lot of its own shape-changing movement to heat)
o a shape that makes the material highly resonant (long and thin is good but wrapped into a box with an aperture is better - like a violin body or a drum)
o a resonant frequency that is within the audible spectrum (generally for a given material this depends on the size of the object you make out of it)
o a shape that imparts some energy (usually as much as possible) to the air (so you cam hear it)

and as tuning forks show steel can be pretty good.

I hope some of that helps.

Originally Posted by MrPiano

Hey! I was just wondering if someone could enlighten me about acoustic frequencies. I'm writing a story and would like to know if iron or steel [swords] have resonant frequencies... and in addition, if they do, how much they would vibrate [and what affects how much they vibrate?]. thanks!

It depends on a great deal but short answer is "yes," and the long answer is "Good luck in demonstrating it with a sword."

Now, if you want to ask about bridges...