Experiment of The Month
Speaker Resonance and Decay Time
Three senior physics majors, Cody Borigo, Kevin Dougherty, and Darren Scott, studying waves in our advanced laboratory course. While investigating a Brillouin zone boundary in a one dimensional lattice (built on a length of piano wire) they drove the system acoustically with a loudspeaker attached to the wire. They detected the lattice response with an identical speaker attached to the other end of the wire.
They observed the frequency shift at the zone boundary, but also saw an unexpected "hump" in the signal strength as a function of frequency. The anomaly turned out to be due to a resonance in the speakers, as they showed in the following experiment.
The power coupled from the bottom speaker to the top is maximum at 30 Hz, and the width of the power peak is 15 Hz. This width predicts a ringdown time of 1/15 = .067 seconds. The students tested this prediction by tapping the speakers to start a resonant vibration.
The data points were collected from an oscilloscope trace of the speaker out put. The line is a fit to an exponentially decaying sine oscillation, with natural frequency of 31.7 Hz and decay time of .0625 seconds, close to the prediction.