Frequency shifts of cantilevers vibrating in various media

A simple model is presented for rectangular cantilevers when vibrating in various media. The mass of the surrounding medium affected by the motion of the lever is calculated. It depends on the dimensions of the lever, on the excited mode, and on the density of the medium. Although the viscosity of the media is not taken into account, the resulting predictions for the resonance frequencies agree well with experimental data obtained for levers in air and water up to the seventh harmonic.