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I read in many posts that the acoustic impedance of a material is usually defined as $Z = pc$, where $p$ is the density of the material under consideration and $c$ is the speed of sound in that material. However, this is the "Characteristic specific acoustic impedance" as explained here:

https://en.wikipedia.org/wiki/Acoustic_impedance

I wonder how the acoustic impedance of a material is related to its dimensions, expecially the thickness.

E.g. if I have 1-atom-thick layer of copper, does this offer the same acoustic impedance of a 1 meter thick layer of copper? I guess that in that case I will have to refer to more general law.

Moreover, how does the acoustic impendace change with the frequency of the acoustic wave? E.g. Does a 100Hz acoustic wave that is hitting a certain material see the same acoustic impedance of a 1MHz acoustic wave hitting the same material?

Thank you in advance :)

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  • $\begingroup$ Hi Gabriele, welcome to the Physics SE. Please use the MathJax syntax for better readability of the formulas in your post. $\endgroup$ – flaudemus Mar 14 at 17:18
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The acoustic impedance of an atom is meaningless. The acoustic impedance describes the response of a medium to the propagation of some acoustic excitation. Are you implying a sound wave that propagates through an atom? Anyway, the classical acoustic theory is developed for continuous media so you cannot expect it to work at atomic scale.

Now, within the limits of macroscopic media, the acoustic impedance can be defined for a medium (what you mentioned as specific impedance) or for an object (for example, the membrane of a speaker). The specific impedance does not depend on the geometry of the medium (like density does not depend on the size of the object). But the impedance of the objects of course it's a function of size and shape. It may depend on frequency too (for speaker membranes for example it does, in general).

If you want to know the specific variation of impedance with geometry and frequency you need to look up some research papers for the specific geometry. You may find relatively easily the results for a disk (or piston) which is one the usual examples in acoustics textbooks.

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  • $\begingroup$ Sound travels though monolayer graphene just fine, and it more or less like an ideal membrane on acoustic length scales. I wouldn't call the impedance of a monolayer meaningless. $\endgroup$ – KF Gauss May 28 at 2:37
  • $\begingroup$ Did I say that the impedance of a membrane is meaningless? $\endgroup$ – nasu May 28 at 11:23

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