Calculating the energy loss due to sound emission on collision

[Voekov]

Homework Statement

I am writing my Extended Essay for IB, where I look at the possibility of obtaining accurate results in open system of a school, by accounting for all energy losses that occur during the investigation.

Before conducting my experiments (which included an air track with two colliding vessels, followed up by 2 'frictionless' vessels on a track), I found the following equation for calculating the energy of sound:

Where:
p - sound pressure
v - Particle velocity
ρ0 - density
c - sound speed
In my case, the values are as follows:
p - 6.324*10^-2 Pa
v - 1.531*10^-4 ms^-1
ρ0 - 1.204 kgm^-3
c - 343.26 ms^-1

Homework Equations

Is this formula valid? If so, how do I solve this integral? The integral does not remind me of anything I have seen so far. I also cannot find any other reference to this formula besides wikipedia (http://en.wikipedia.org/wiki/Sound_energy)

The Attempt at a Solution

I did visit the maths and physics departments in my college. Neither was able to help me. Maths department stated this formula doesn't even look correct, while the physics department told me to ask somewhere else.

 

[Pi-Bond]

It seems to be a integral over a volume of some sort. Anyhow this is the first time I've seen such a formula. Also the wikipedia entry has no citations at all...you may be better off devising another approach. If you have minimized losses to friction, you could compare the kinetic energies before and after collision to get an estimate of the energy lost as sound.

 

[Voekov]

That is the point of my investigation. What I am doing, is trying to account for all the possible energy losses by measuring and calculating them. I have calculated losses to friction, losses in form of heat loss due to a forced inelastic collision (temperature change of deforming Blu-Tack, which was used to keep the vessels together once they collide), and now I need to calculate the energy output of the sound level. Then, when I add them up and subtract from the initial kinetic energy value, I hope to obtain a result reasonably close to the final KE level.

Is there any other way to calculate the energy required to generate given volume of sound? I did some research and all I found was really difficult university-grade jargon.

 

[Pi-Bond]

I see your point now. But if you can't find a (veritable) formula, I think the only way is to change your approach. How about making the collisions happen in vacuum? My school had some tools to achieve vacuum in a closed volume. Maybe yours does too? This way you could eliminate losses due to sounds totally.

 

[Voekov]

That would mean I am to scrap the idea of air resistance as well, which would pretty much leave me without a topic. I will continue looking for that formula then.

 

[PeterO]

That would mean I am to scrap the idea of air resistance as well, which would pretty much leave me without a topic. I will continue looking for that formula then.

Going to make an air-track hard to operate as well!

 

[Voekov]

Hah, that's true :)

 

[PeterO]

I see your point now. But if you can't find a (veritable) formula, I think the only way is to change your approach. How about making the collisions happen in vacuum? My school had some tools to achieve vacuum in a closed volume. Maybe yours does too? This way you could eliminate losses due to sounds totally.

Interesting concept. Are losses we put down to sound energy loss due to the sound traveling away from the source or because the source went through the motion that would usually make the sound.

When we put electrical energy into a loud speaker, sound is produced.

If the speaker was placed in a vacuum no sound is heard, but was it produced.

Would the the I-V fuigres of the attached amplifier system show the reduced power requirements?