# The sound energy when two or more objects collide

When two objects collide in an inelastic collision, some kinetic energy is converted to sound energy and heat. How do I determine how much of the kinetic energy is converted to sound energy? Provided that I'm doing an experiment where I take the readings as seen in this question's answer.

I have tried to use the law of conservation of energy to do this:

$KE_{1i} + KE_{2i} = KE_{1f} + KE_{2f} + Sound Energy + Heat$

Since there is heat generated here, I cannot just compare the initial and final values of the kinetic energies. So, after reading this question and the answers I can now have an idea what the formula of the sound energy might be like.

$E\ \alpha\ \omega^2A^2$ where $\omega = 2\pi f$

thus I can say $E\ \alpha\ 4 \pi^2 f^2 A^2$ ?

One problem is that the formula I found here is a proportional formula not a direct formula that is using an '=' sign so there might be some more constants added to the relationship.

I have read somewhere else that I am supposed to use sound energy density instead of sound energy, but I'm not sure if sound energy density could represent the whole energy conversion from kinetic to sound.

In addition, the reason I want to find the energy using frequency and amplitude as variables is that I want to see quantitatively the effect of increasing the speed of the objects to the amplitude of the sound produced. I know that every material has its own natural frequency on collision as seen from the coin dropping experiment.

So, what is the 'proper' way of finding the relationship between the amplitude and the speed of the objects (kinetic energy I suppose)?