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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)?

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How much sound colliding objects make depends entirely on the objects and the medium they are in. In the vacuum of space collisions don't make a sound, at all. In Earth's atmosphere the total energy of sound released by collisions that are caused by solid objects is very small compared to the energy of the objects. This is because of the large difference in density between solids and the atmosphere.

In water, however, this is entirely different, again, because the density of water is of the same order of magnitude as the density of the solids. The "sound" of an underwater earthquake is a tsunami and we have seen twice recently just how much energy can be set free in form of those tidal waves.

In short, there is no general formula, it all depends on the details of the collisions and the answer can range from nothing to near 100% of the incident energy if the densities of objects and media are matched.

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