On the vibrations of an elastic plate in contact with water

In connection with the problem of submarine signalling the question arose as to the pitch of the fundamental note of a thin circular plate or diaphragm of given material and dimensions, filling an aperture in a plane wall which is in contact on one side with an otherwise unlimited mass of water. The following investigation, which includes some extensions, is now published by permission. To simplify the theoretical treatment, the wall is supposed to be rigid, and the plate to be firmly clamped to it along the circumference, although these conditions are only imperfectly fulfilled in practice. Even with these limitations an exact solution is out of the question, but a sufficient approximation can be obtained by Rayleigh’s method of an assumed type, which gives good results if the type be suitably chosen. It is known that the frequency estimated in this way will be somewhat too high.