Abstract
A review of textbooks and research literature reveals that there is room for improvement in the treatment of this simple but important bore shape. We use plots of acoustic pressure standing waves to show students in a descriptive course that a complete cone and an open pipe of the same length have the same natural frequencies. These plots also predict the qualitative behavior for the frequencies of a frustum closed at the small end and suggest a rigorous approach to their calculation. Incorporating the open end correction for a straight pipe plus a correction for viscosity and thermal conductivity in the calculation results in agreement with experimental values to within 0.5%. In order to understand the inharmonicity of the frustum's frequencies from a different approach, we have calculated the pressure impulse response for reflection from its closed end. We find that this consists of a delta function plus an inverted, exponentially decaying wake. Experimental observations confirm both that shape for the impulse response and its contribution to the evolution of the waveform through several reflections.
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