This award supports two related projects within the context of musical acoustics. These represent two complex problems involving energy transfer in metal structures. In the case of impacted plates, it has been shown that equations developed in the 19th century can be used to describe the steady-state motion of thin plates with some success. However, predicting the transient response of plates to an impact has proven to be a less tractable problem. The work supported here will lend insight into the physics of the struck plate, primarily by comparing experimental work to the results of computational modeling. The interaction between vibrating air and the walls that contain the air is likewise a complex problem of broad interest. Several possible explanations have been posited to account for the audible effects reported in the literature, but as of this date none have been supported by experimental data. The primary goals of this work are to understand the transient response of struck plates within the context of idiophones, and to determine how structural vibrations affect the sound of brass wind instruments. he study of musical instruments is interesting to undergraduate students, and therefore, having a research program in this area naturally attracts young minds. While the systems under study involve musical instruments, the research centers on studying basic physical phenomena which are not unique to musical acoustics. Thus, students are introduced to important scientific research through a subject they find fascinating.
The most important outcomes of the supported research are the experiences that the undergraduate students had in the laboratory. Over the three-year period of the grant, seven students participated in research along with a local high school teacher. During that time five peer-reviewed articles were published and six presentations were made at national and international conferences. The articles were coauthored by the students and the high school teacher, and the students made most of the presentations at the conferences. Scientifically, the key outcome of the work was a deeper understanding of some basic science. Specifically, the project resulted in a deeper understanding of how vibrations of the metal walls of brass wind instruments affect the sound produced. This knowledge is applicable to the manufacture and performance of trumpets, trombones and tubas, but it is also applicable to any situation where there is air flow through pipes or ducts, including many industrial and manufacturing situations. Additionally, studies of struck flat plates in the context of percussion instruments have demonstrated that a key theory that is usually presented as being universally applicable to thin plates is not. Normally, if a plate is thin it can be modeled in a much more simple way than a thick plate. However, in the course of this work it was shown that the theory normally applied to thin plates can fail. The failure of the theory can occur in some very common situations, including situations in which it is often used for analysis. Finally, two new techniques for imaging micrometer-sized vibrations were developed. One method, termed speckle subtraction imaging, holds promise for detecting subterranean objects because the process is useful in cases where sand is in motion. For example, when a metal object is buried under sand it can be made to vibrate using sound; this method of imaging can be used to locate the position of the object unambiguously by detecting the minute motion of the sand above the object. The second imaging system that was developed was for educational purposes. It provides an affordable method for teachers to demonstrate how objects vibrate by viewing the vibrations on a computer screen in real-time. Publications resulting from the work: Daniel W. Zietlow, Donald C. Griffin and Thomas R. Moore, "The limitations on applying classical thin plate theory to thin annular plates clamped at the inner boundary," AIP Advances 2, 042103 (2012). Thomas R. Moore, Ashley E. Cannaday and Sarah A. Zietlow, "A simple and inexpensive optical technique to help students visualize mode shapes," Journal of the Acoustical Society of America 131, 2480-2487 (2012). Ashley E. Cannaday, Brandon C. August, Thomas R. Moore, "Tuning the Nigerian Slit Gong," Journal of the Acoustical Society of America 131, 1566-1573 (2012). Wilfried Kausel, Daniel W. Zietlow and Thomas R. Moore, "Influence of wall vibrations on the sound of brass wind instruments," Journal of the Acoustical Society of America 128, 3161-3174 (2010). Thomas R. Moore, Ashley E. Cannaday, and Sarah A. Zietlow, "Imaging of vibrating objects using speckle subtraction," Journal of the Optical Society of America A 27, 1863-1867 (2010).
