1. Resonance & Standing Waves
Waves & Sound
Resonance & Standing Waves

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

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