Why do some metals ring when struck while others don’t?
In: Physics
Tons of wrong answers or partially correct answers in here. I’ll chime in, as I am a specialist in vibration of metallic structures.
Natural frequency depends not only on material properties, but physical arrangement and constraint as well. Consider a bar made of 6061-T6511 aluminum. If you clamp it at one end and strike the middle with a mallet, you’ll get a totally different response than if you clamp it at both ends and strike the middle with a mallet. The natural frequencies will depend on the choice of material, the dimensions of the bar, and the method of constraint. The response will depend on both the natural frequencies and how the bar is excited (where, how it is struck).
Real structures have multiple (infinite in fact) natural frequencies. If you want to design something to be useful in producing musical tones, you want to come up with something that has a fundamental (lowest) natural frequency that corresponds to some particular note, such as 440 Hz for concert A4, and upper natural frequencies that are well spaced or if possible integer multiples of the fundamental frequency. When you excite it, the response is going to contain a combination of the natural frequencies, so you want to design it such that the fundamental is a strong contributor, and other frequencies that aren’t multiples of the fundamental are weak contributors. Simple structures are good for this, and you can choose the clamping points carefully to try and get more harmonics to be multiples of the fundamental. Taught strings and xylophone keys work well. Structures like circular membranes don’t work well for producing tones, since you’ll get a jumble of diasonant frequencies in the response and this is why drum heads don’t tend to produce as distinct tones as other instruments.
Beefy structures or structures made of stiff materials will, in general, will have really high and diasonant frequencies, so you’ll hear a clang or thud when you whack it. Sometimes you get lucky and find a structure that makes a nice sound when you excite it, but it’s not entirely material dependent.
Material damping will play a role in how sustained the tone is, if you get one. For this reason, some materials will sound inherently better even if you nail the configuration for producing a tone. This is why you see different woods, for example, being prefer in crafting quality instruments.
Designing structures to have certain frequencies requires knowledge of structural dynamics. This is one of my areas of expertise, as I design aircraft components for a living. We design for frequencies not to produce certain tones, but rather to not coincide with frequencies from rotor blades or rotating engine components.
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