# Physical scale at which the equations of acoustic impedance can be applied?

This question follows from a previous SE question asking how the thickness of a material affects the acoustic transmission coefficient.

This website seems to suggest that the equations defining the compliance and inertance components of specific acoustic impedance ($z$) are dependent on a certain assumption of scale:

Both use the idea of a compact region: a region whose dimensions are much smaller than the wavelengths we are considering.

Further searching suggests this simplifying approach is also sometimes called acoustical compactness:

The ‘size’ of the body at a given frequency is called its compactness and is characterized by the parameter $ka$ where $a$ is a characteristic dimension, or by the ratio of characteristic dimension to wavelength $a/λ$. A compact source, one with $ka ≪ 1$, radiates like a point source, while non-compact bodies must be treated in more detail, as we saw in the case of a sphere in §2.1.

Does this mean the usual equations describing acoustic impedance cannot be applied when a media layer has thickness $a \ll \lambda$ ? I can imagine that pressure starts to become more complicated to describe at this scale, but how exactly is the assumption involved?

• Thanks Niels, that's very close to what I'm looking for, and incidentally I agree with you so far. However, the previous question was asking about very thin plates (I think they said 100 Tungsten atoms, or ~ $1.35 \times 10^{-8} \ m$ thick.) Given this more specific example, does your answer mean this very thin sheet would only begin to impede waves with frequency $\gt$ 74 MHz? I guess I can also imagine the pressure wave deforming the sheet as well, instead of causing it to vibrate? – D. Betchkal Dec 21 '17 at 18:31