High Speed Photographic Analysis of Waves on a Guitar String

Efforts were made to examine the accuracy of a linear model for the behavior of a string, fixed at its endpoints, when it was subjected to an initial displacement and allowed to vibrate freely. The model relies on multiple approximations, but offers exact solutions for the waveform in both space and time.

The study of waveforms applies to many areas of physical phenomena, and therefore becomes crucial in developing a thorough understanding of the laws of nature. Wave-based models appear in a wide variety of physics subjects, from classical motion and mechanics to electricity and magnetism, optics, and quantum mechanics. It is equally important, however, to be aware of of the limitations of certain wave-based models as they apply to modeling the behavior of real physical systems under experimental constraints.

Figure 1

With the advent of more sophisticated forms of digital photography, it has become possible to further investigate the behavior of a vibrating guitar string as it varies in both space in time. Using a Casio EX-F1 DSLR digital camera, video of the vibrating string was recorded at 1,200 frames per second. This not only gives a unique look at the string's behavior that is unthinkable to those who first addressed classical wave motion during its theoretical development centuries ago, but it also allows for more quantitative analysis to be performed in order to compare the motion to predicted models.

Figure 1 above shows an edited still frame taken from high speed video recording. The string shown is at its initial displacement from rest just before release. Each frame from the high speed video was edited until it looked similar to this image, so that spacial coordinates could be systematically taken from them. This was done for one period of motion in time, approximately 20 frames per sample, and will be further discussed in the "Apparatus" section.