Resonance & Standing Waves

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Presentation transcript:

Resonance & Standing Waves Waves & Sound Resonance & Standing Waves

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

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.

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

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.

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? What would be the next two resonant frequencies of the system? *assume vsound = 340 m/s

HOMEWORK ** vsound = 340 m/s Determine the first three resonant frequencies of a 1.5m closed at both ends air column. [A: 113.3 Hz, 226.6 Hz, 340 Hz ] What is the length of an open at both end air column if its 5th harmonic frequency is 1250 Hz? [A: 0.68 m] Determine the 7th and 9th harmonic frequencies of a 3.5m closed at one end air column. [A: 170 Hz, 218.6 Hz]