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A vibrating system has a characteristic spectrum, a set of frequencies at which the system gives a large response. For instance, a washing machine with an unbalanced load will only get seriously out of whack at certain rates of oscillation. At these natural frequencies the system exhibits special characteristics, including nodes (on a vibrating string, for instance) and nodal lines (seen as areas where sand collects on a vibrating plate) where there is no oscillation. It turns out that one can measure Doppler shifts at these lines and then apply simple mathematical formulas to learn much about the physical properties of the vibrating system. The author has developed just such formulas for vibrating membranes and discusses such interesting applications as the design of turbines.

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