Comparing Experiments to Models: Vibrating Guitar Strings
“An experimental analysis of a vibrating guitar string using high-speed photography,” by Scott B. Whitfield and Kurt B. Flesch of the University of Wisconsin – Eau Claire seeks to compare the waveform of a plucked string with a standard wave model of this vibration at various initial amplitudes and locations along the string. Whitfield and Flesch conclude that the experimental vibration matches well with the model when the string is plucked at small amplitudes. This detailed but relatively clear article contributes to physics due to its novelty and solid experimental design.
The method that Whitfield and Flesch used in order to make these comparisons is fairly simple, but is quite effective. First, they constructed a quasi-guitar using only one string and wooden boards (in order to enhance the visibility of the string). Next, they set up the remainder of the experiment, and then plucked the string at three separate locations: the middle of the string, 1/3 of the way from the string’s end, and 1/5 of the way from the string’s end. At each location, they made three plucks, each one at separate heights. When the string was plucked, they captured the string vibration using high-speed cameras and a computer program. Once they had captured the data, they compared the vibrating string to the model using both equations and the recorded images as an overlay on the model.
From this experiment, they were able to determine that the experimental pluck aligns most the model at smaller amplitudes, regardless of the location of the pluck. They also determined that at larger initial amplitudes, the experimental vibration strayed more from the modeled vibration. They argue that the string’s construction, including its material and tightness, had a greater effect on the larger plucks, which is why there is more variance from the model.
While this article could have explained its use of the equations slightly more, it was wholly clear and comprehensible. It also contributes heavily to the field, breaking new ground. No studies that compare a vibrating string to a standard wave model had been published prior to this one. This study is solid because it is consistent with previous knowledge (it cites Arthur Benade’s use of equations). But, while the data supports the conclusions drawn, Whitfield and Flesch made several assumptions regarding the decay of the strings and the string’s curve at the initial amplitude. They acknowledge these assumptions in their writing, but the effects that they assumed were negligible perhaps could have had an effect on the experimental vibration.
Thus, Whitfield and Flesch’s study concludes that, after comparing an experimental string’s vibration to a standard wave model, the vibrations most match at smaller initial amplitudes. This study is clear and definitely breaks new ground, which is what makes it good for physicists studying vibrating strings.
References
Whitfield, Scott B., Flesch, Kurt B. (2014). .An experimental analysis of a vibrating guitar string using high-speed photography. American Journal of Physics, 82; doi: 10.1119/1.4832195
