In my medical physics book it says that Intensity is 1/2 a2/pc=a2/2z Where a is the amplitude, p medium of density, c velocity of that wave and offcourse Z is the impedance. When I google it it just comes up that intensity of sound waves are proportional to the pressure of a area. Could someone pleas explain me this equation if that is the case?
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Sound waves are pressure waves. We measure it as a logarithmic ratio of intensity. Sound intensity is a useful parameter to measure because it's related to the energy incident on a surface which can be easy to measure. Sound intensity is proportional to pressure squared. When calculating decibels we would have to handle that like so: \begin{equation} I = p^2/Z \end{equation} for some constant of proportionality k \begin{equation} 10log(I_1/I_0) = 10log(Zp_1^2/Zp_0^2) =20log(p_1/p_0) \end{equation} where p1 is the wave pressure and p2 is the ambient or reference pressure.
The equation you have quoted is simply one that equates the impedance to \begin{equation} c\rho = Z \end{equation} If you wish to understand where that comes from google the derivation of the acoustic wave equation. Really it's just a property of the medium that determines the relation ship between pressure particle velocity and energy.
