# What is sound intensity?

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?

## 1 Answer

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: $$I = p^2/Z$$ for some constant of proportionality k $$10log(I_1/I_0) = 10log(Zp_1^2/Zp_0^2) =20log(p_1/p_0)$$ 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 $$c\rho = Z$$ 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.