# How do I find the energy of sound from Audacity?

For a project, I recorded the sounds of a boccee ball impacting with some ping pong balls in a container using Audacity. I also used a sound pressure level meter to record the maximum dB C that was produced from the impact. How do I analyse this data to find the energy in the sound wave.

I don't know if you can do this directly in Audacity. But you can process the signal to estimate what you want as follows.

1. Compute the amplitude of the signal from the sound pressure level.

2. Normalize your signal to have an amplitude according to the previous step.

3. Compute the time integral of the square of your signal.

If you use SI units you should obtain a value in Joules.

Probably use some kind of reference sound. You can play a tone, and than use app for your mobile phone, to measure, how loud the sound is. How is app for your mobile phone calibrated is than another question. Another way would be, to have a simple tone generator and measure, how much power does it consume (eg. buzzer connected to 9V battery). Then you make approximation, that almost all energy is transferred to sound (not nessesery true). But then you must take into account some facts:

1. Audacity measures amplitude of signal voltage as function of time. The correlation between voltage and air pressure is not necessary linear.
2. Sound is produced as combination of signals with different frequencyes. Energy of waves depends on frequency. You can either make Fourier transform and integrate it as $$\int E(\nu) d\nu$$ or calculate energy numerically.
3. Sensitivity of sensor (microphone) is generally function of frequency $$\nu$$. You have to compensate that.
4. Distance between source(speaker) and microphone is important.

So, given nature of your project I would either connect small speaker on Arduino or buzzer to battery, measure current and voltage using multi-meter, and calculate power used, and say, that this is energy of sound waves. I would put microphone directly next to reference speaker/buzer and calibrate scale in audacity in units of pressure amplitude (can be calculated back from power used to drive speaker). Then I would found the lowest frequency of your sound (generally is the loudest) and assume, that you have only signal of that frequency, and calculate energy from frequency and pressure amplitude. I would ignore point 3.

BUT, If you are recording sound of balls it is likely, that you will find some shock waves (N-wave) or other weird-shaped sound-waves. In that case you would generally need to make Fourier transform numerically or make some kind of ugly approximation.

Probably check Google play for some app. There might be something which shows energy of sound, between all guitar tuners, "make physics laboratory from phone apps" etc...

Bear in mind that neither phone app or Audacity aren't calibrated. If you have some simple school project, potential app (decibel meter) should be ok, but If you want to know the real value of energy, you should calibrate your microphone somehow.

• Sorry, I missed that you are already using dB meter. So calibrate your setup with it. But not with sound of balls, which will be wierd-shaped, but with sine wave. After that you have calibrated Auacity measurement. – Vid May 4 at 22:35