Daniel W. Zietlow

Influence of wall vibrations on the sound of brass wind instruments

The results of an experimental and theoretical investigation of the influence of wall vibrations on the sound of brass wind instruments are presented. Measurements of the transmission function and input impedance of a trumpet, with the bell both heavily damped and freely vibrating, are shown to be consistent with a theory that assumes that the internal pressure causes an oscillation of the diameter of the pipe enclosing the air column. These effects are shown to be most significant in sections where there are flaring walls, which explains why damping these vibrations in cylindrical pipes normally produces no measurable effects.

The limitations on applying classical thin plate theory to thin annular plates clamped on the inner boundary

The experimentally measured resonance frequencies of a thin annular plate with a small ratio of inner to outer radii and clamped on the inner boundary are compared to the predictions of classical thin-plate (CTP) theory and a finite-element (FE) model. The results indicate that, contrary to the conclusions presented in a number of publications, CTP theory does not accurately predict the frequencies of a relatively small number of resonant modes at lower frequencies. It is shown that these inaccuracies are attributable to shear deformations, which are thought to be negligible in thin plates and are neglected in CTP theory. Of particular interest is the failure of CTP theory to accurately predict the resonance frequency of the lowest vibrational mode, which was shifted approximately 30% by shear motion at the inner boundary.

Transient motion of a circular plate after an impact

The transient response of a flat circular plate to a sudden impact has been studied experimentally and theoretically. High-speed electronic speckle pattern interferometry reveals the presence of pulses that travel around the edge of the plate ahead of the bending motion initiated by the strike. It is found that the transient motion of the plate is well described by Kirchhoff thin-plate theory over a time approximately equal to the time required for the initial impulse to circumvent the plate; however, a more sophisticated model is required to describe the motion after this time has elapsed.

Searching for early reflected waves after strike of Caribbean steelpan using time-resolved electronic speckle pattern interferometry

Electronic speckle-pattern interferometry has become a popular tool for studying the operating deflection shapes and normal modes of musical instruments. Normally, ESPI is used with cameras having frame rates below 50 Hz, and the resulting interferograms are the result of a time average over many oscillations. Using ESPI with a high speed camera operating at frame rates of several thousand frames per second allows for time-resolved examinations of transient motion, and this technique has been used to study the motion immediately following the strike on a Caribbean steelpan. Caribbean steelpans are a complex system of coupled oscillators and it has been suggested that the inflections from the concave shape of the steelpan bowl to the convex shape of the note areas serves as a boundary where mechanical waves are partially reflected. High speed ESPI movies of strikes on a low tenor steelpan were acquired in an effort to search for evidence of these reflected waves.

Modeling orchestral crotales as thin plates

Orchestral crotales are designed in such a way that the overtones become less harmonic as the fundamental pitch increases. Deutsch, et al. used Kirchhoff-Love theory to show that by eliminating the central mass and choosing the correct ratio of inner to outer radius the overtones can be harmonically related (J. Acoust. Soc. Am. 116, 2427 (2004)). However, when a crotale was constructed using this design, the overtones were not harmonically related. We show that this lack of agreement between theory and experiment is due to the fact that shear motion of the inner boundary, which is neglected in classical thin-plate theory and thought to be unimportant, can significantly affect the resonance frequencies of plates even when they are extremely thin.

High speed electronic speckle pattern interferometry as a method for studying the strike on a steelpan.

Electronic speckle pattern interferometry (ESPI) is a useful method for characterizing the operating deflection shapes and modes of vibration of musical instruments. Using ESPI in conjunction with a high‐speed camera, capable of capturing images at rates of several thousand frames per second, allows for time‐resolved examinations of transient motion. High‐speed ESPI movies of note strikes of a low‐tenor (also called a soprano) steelpan were acquired while simultaneously recording the sound of the strike. The comparison of the time‐resolved interferometry data with the analysis of the sound recordings allows for insights into the evolution of coupling between note areas.

The auger shell whistle.

We report on investigations of a musical instrument made from the shell Terebra Turritella, or auger shell. To our knowledge, this instrument has been developed only recently. The instrument is played from the large end using an edge tone, and a diatonic scale is achievable merely by drilling five tone holes in a straight line down the length of the spiral shell. It is surprising that a naturally occurring cavity can produce a diatonic scale, and implies that there is something special about the shape of the auger shell. However, experimental and theoretical investigations reveal that the auger shell does not actually have such a resonance structure.

High‐speed electronic speckle pattern interferometry of a struck flat plate

An electronic speckle pattern interferometer capable of imaging 33,000 frames per second has been used to study the transient motion of a flat plate which was struck at a point near the edge. Multiple interferograms, each with an exposure time of 25 microseconds, were combined to construct a video of the plate motion that can be used for both qualitative and quantitative analysis. The interferograms reveal the expected evolution of the bending waves created when a thin circular plate is struck near the edge; however, anomalous displacement of the surface of the plate is also observed. This unusual displacement of the surface takes the form of a transverse wave that precedes the motion directly attributable to the normal propagation of the initial bending wave.

How can bell vibrations affect the sound of brass instruments

It has recently been shown that the vibrations of the bell of a trumpet affect the spectra of the sound produced during play. The manner in which these vibrations produce this effect is still under investigation, but two possibilities have been proposed: (1) the vibrations of the bell feedback to the lips and change their motion, and (2) the bell vibrations change the radiation impedance of the instrument. The former explanation appears to be the most plausible; however, we will present results of recent experiments that indicate at least some of the effect is due to a change in radiation impedance.