Please excuse the perhaps obtuse question, but if one knows the speed of propogation of sound through a particular material (metres per second) and its impedance (Rayl x 10 -6) is there any relationship that can be drawn with respect to a resonant frequency for that material irrespective of its physical size?
Claus Jensen
No, because if it had a resonant frequency, and you took a bigger piece of the same shape, with the same constitutive parameters, the resonant frequency would be decreased.
-- john
'Resonant frequency' is a bit more complicated for mechanical oscillations, there's more than one. For a thin rod, they're at frequencies that correspond to the length being multiples of a quarter-wavelength for sound in the material, or maybe half-wavelength depending on how the rod is mounted. Thus, the sonic velocity allows you to calculate the (base) resonant frequency easily, the impedance doesn't come into it. Impedance will goven whether you have a stiff or a non-stiff system, eg. tool steel or rubber.
For other shapes the relationship between size and resonance is more complicated, search for 'chladni plates' (not sure of spelling).
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