Intensity Of Sound

I know that intensity of sound at a distance 'r' from the the source of sound is given by the equation (i) in the image. Also the second equation gives the wave intensity, but at what point or distance from the source this intensity is?? *As we can see the every term in the equation (ii) remains constant and not change with the distance.

• What are the variables inside the brackets in your second equation? – John Rennie Sep 28 '16 at 6:23
• 'V' is velocity of the wave in the medium, 'w2' is the angular velocity of wave and the that remaining one is the density of given medium. – Avi Sep 28 '16 at 7:16
• In that case the $r^{-2}$ dependence is in $S_m$ i.e. $S_m = S_0/r^2$ for some constant $S_0$. – John Rennie Sep 28 '16 at 7:22
• from your conclusion, $Sm=S0/r^2$, i.e. we can say that amplitude Sm is inversely proportional to square of distance from source. but we know intensity (I) is directly proportional to square of amplitude ($Sm^2$) and also from my first equation (I) is inversely proportional to ($r^2$). from these two we get $Sm^2$ is inversely proportional to $r^2$ i.e Sm is inversely proportional to r, which is against your conclusion that Sm is inversely proportional to $r^2$. Please explain – Avi Sep 28 '16 at 9:38
• I just want to know that if you have been given all numerical values of all variables in the equation (ii). Example value of each variable in equation (ii) is 1 and you are asked to find out intensity of wave at a distance of 5m from the source using equation (ii) then how will you find it. – Avi Sep 28 '16 at 9:49