I teach high school physics and we spend some time talking about waves and sound. I've found that one of the best ways to do this is to use free software to analyze the harmonic components of various sounds and then to rebuild them one frequency at a time.
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
1. Computer with microphone input
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
Load up Visual Analyser and make a sound into the microphone. Be sure to watch the lower window. That's the FFT (Fast Fourier Transform), it shows us the frequencies being produced.
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
Now that we have our data we can try to reproduce the sound. This is where you'll need Audacity. Once you've opened Audacity just go to the "Generate" menu and select "Tone".
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
In order to add your other frequencies you must first create a new track. If you don't Audacity will simply append your new tone to the end of the first one. So, for each new tone you add you must first go to the Project menu and select "New Audio Track".
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, what's the problem? Go back to Visual Analyzer. Un-click "Hold" and hit your beaker again. What do you see in the FFT window? The different frequencies drop off very quickly, with only the loudest one (which happens to be the 2nd Harmonic) lasting any appreciable amount of time.
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
So, so all we need to do is select "Fade Out" from the "Effect" menu. The result is not really very adequate, but if you repeat the fade two more times it ends up being pretty good.
Step 7: The Final Product
I wish I could get a good recording of my whacked beaker, but this one will have to do.
"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.