We are able to talk about, not only about how various frequencies combine, but also how the sounds begin and decay to result in what we hear.
Step 1: Stuff You Need
2. Microphone you can plug into the computer
3. Audacity. http://audacity.sourceforge.net/
4. Visual Analyser - Free oscilloscope program for Windows. http://www.sillanumsoft.com/
5. Something to make a sound. I've found a beaker struck with a pencil eraser works great.
Step 2: Determine the Harmonic Components of Your Sound
You'll notice the peaks appear and go away very quickly. I'm using a beaker struck by the eraser end of a pencil. If you want to capture the peaks, just click in the "Hold" check box. The FFT window will then retain all the peaks. Once you've managed to get some good peaks you'll need to turn the scope off. If you don't you'll make some noise and all your peaks will be gone (trust me on this).
Simply click on the peaks of interest in your FFT window and VA will tell you the frequency. For something like this I usually grab 3 to 6 of the most prominent peaks. For mine in descending order of peak height (loudness): 1680 Hz, 4380 Hz, 3330 Hz, 7420 Hz. I could grab more, but these four main frequencies ought to do.
Step 3: Begin Rebuilding the Sound
A window will pop up. Keep Waveform as Sine and set frequency to the first frequency on your list. You'll also need to change amplitude. If you leave it at 1.0 then when you add the other frequencies you'll end up with a very distorted sound. I've found 0.3 is a good level for the loudest frequency.
After you've generated your frequency click play. It should sound similar to your sound, but it is easy to tell it's different.
Step 4: Add Your Other Frequencies
Once you've done that simply "Generate" you new "Tone". Get your second loudest frequency and add it in. Set the amplitude a little lower with each frequency you bring in.
Repeat this process for each frequency you wish to add. Hit play and you'll hear a horrible din. I've attached mine so you can hear it. It doesn't really sound like a beaker at all.
Step 5: Making It Sound Right
So, lets go back to Audacity and trim our sounds. Simply click and drag over the region you don't want and then hit the delete key. I'll let the first frequency last for around half a second and trim the others down to around a quarter of a second.
Hit play again. I've attached mine again. It still doesn't sound right. There's a simple reason for that. The beaker doesn't stop vibrating instantly. The frequencies being created are damped out, they decay more slowly.
Step 6: Lets Fade It Out
Step 7: The Final Product
"Actual Beaker" is a recording of me hitting a beaker. I really need to get a better microphone.
"Done Beaker" is the exported version I created in Audacity.
"Done Beaker with noise" is the same version with a little white noise (created in Audacity) to make it sound like my poor recording.