Musical Acoustics of Orchestral Water Crotales

An experimental investigation of orchestral crotale vibrational modes in water is presented, along with a qualitative virtual mass model describing the observed effects. Changes in frequency, overtone ratio, and mode splitting as a function of water depth are reported for a C6 crotale using electronic speckle-pattern interferometry. These data are related to perceived changes in pitch and timbre, along with the creation of audible beats at particular water depths. It is also shown that the suspension method used by musicians when dipping crotales into water leads to the creation of additional acoustically significant modes that are not excited when the crotales are mounted in the standard manner

Normal Modes of a Musical Drumhead under Non-uniform Tension

The effect of non-uniform tension on the normal modes of musical drumheads is examined. Using the standard (m,n) designation for the number of nodal diameters and circles, ideal circular membrane modes with m\u3e0 are doubly degenerate. These degeneracies can be lifted by perturbations to the circular symmetry. Of practical interest to drummers are perturbations caused by non-uniform tension applied at the rim of the drum, leading in some cases to audible frequency splitting. The role of the (1,1) mode in practical drum tuning is analyzed using data obtained using time-averaged electronic speckle-pattern interferometry along with finite element analysis. The resulting model is then generalized to include all modes, using symmetry arguments along with a selection rule taken from group theory. The model compares favorably with both perturbation theory and finite element analysis, and is consistent with experimental observations

Drum Tuning: an Experimental Analysis of Membrane Modes under slightly Non-uniform Tension

Results of an experimental study of normal mode vibrations in single-headed musical drums under non-uniform tension are presented. Although uniform tension is often assumed in theoretical treatments, in practice the musical drum only approximates this condition, even after careful tuning by the drummer. This study investigates the behavior of normal mode shapes and frequencies under non-uniform tension, as they relate to the tuning process. In particular, the role of the (1,1) mode is described. Experimental results include electronic speckle pattern interferometry (ESPI) images of modal shapes along with the associated frequencies. A finite element model is used for comparison with the experimental results

Chladni Patterns on Drumheads: A “Physics of Music” Experiment

In our “Physics of Music” class for non?science majors, we have developed a laboratory exercise in which students experiment with Chladni sand patterns on drumheads. Chladni patterns provide a kinesthetic, visual, and entertaining way to illustrate standing waves on flat surfaces and are very helpful when making the transition from one?dimensional systems, such as string and wind instruments, to the two?dimensional membranes and plates of the percussion family. Although the sand patterns attributed to Ernst Florens Friedrich Chladni1 (1756–1827) are often demonstrated for this purpose using metal plates,2–4 the use of drumheads offers several pedagogical and practical advantages in the lab