Demonstrates: Sound waves, and pure notes vs harmonics
Description: The bowl makes different tones when it is lightly tapped vs. "bowed" with the suede wand. The free spectrum analysis software Audacity can be used to show students the spectrum of tapped and bowed notes. The tapped bowl has several prominent anharmonic overtones (just like a bell.) However, the bowed bowl creates a steady, repetitive tone ... and thus, from Fourier series, all the overtones must be (and are) perfectly harmonic.
In addition, the bowed bowl may have overtones that are not present in the tapped bowl (for example, a 2nd harmonic). Since the tapped bowl excites essentially all the low lying normal modes, this second harmonic is actually not a normal mode, but simply the result of a high amplitude vibration of the fundamental mode, driving it into nonlinearity. (This discussion might be more suitable for upper division classes!)
Instructions: Place Crystal Bowl on o-ring. Using the suede wand either tap the top edge of the bowl, or run the rod along the outer edge of the bowl.
Items Used: Crystal bowl, o-ring, suede rod.
Notes:Math Description:
Size: 12" diameter Condition: Good. Hazard: Can be loud.
