On the periods of a free-free bar immersed in water

Abstract

If a bar is vibrating under water it will set up circulating currents which possess kinetic energy and so in effect add to its inertia: consequently the frequency under water will be less than the frequency in air. The effect of the water is precisely the same as if the density of the bar had been increased: the apparent increase of mass is usually called the “added mass” of the bar and the total apparent mass the “virtual mass”, and these terms will be used subsequently.