1. Waves & Sound

2. Resonance  Any oscillating system has one frequency in which the system oscillates most easily. This frequency is called the natural resonance frequency. Some examples: ○ Rumble of thunder causing windows to vibrate ○ A “Fresh” 1993 Honda Civic subwoofer

3. Standing Waves  A type of natural resonance, occurs when the reflected wave is timed precisely with the incident wave as to appear not to move.  Regions of standing waves: Node: Regions of destructive interference where the medium does not move (equilibrium) Anti-node: Regions of constructive interference where the medium is displaced at a maximum.

4.  The wavelength of a standing wave is double the distance between two consecutive nodes or antinodes. 0.5 1 1.5

5. Example #1  A standing wave with a frequency of 30Hz is generated in a string that has a length of 10cm (fixed at both ends). One antinode is observed in the standing wave. Find the velocity of the wave.

6. Example #2  A piece of PVC pipe can often be used as a speaker port in a homemade subwoofer box. What minimum length of pipe is required in order to have the system resonate at 50Hz. (assume v sound = 340 m/s)

7. Example #3  What would be the next two resonant frequencies of the system in example #2?