The problem of sound transmission through a membrane stretched across a duct is analyzed rigorously. The integral equation for the velocity distribution of the membrane is set up and studied in the special case of a circular cylindrical tube. Equivalent circuits for the membrane are shown for the frequencies around the resonances and the antiresonances of the membrane. High transmission loss is commonly associated with a large mass, but it is clear that it can also be obtained with very little mass if stiffness rather than mass provides the high impedance.
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Uno Ingård (1954) studied this question.