On the existence of a symmetric acoustic mode in a quadratic solid wedge

It is shown that in a solid truncated wedge whose local thickness depends quadratically on its height, along with the earlier predicted countable set of antisymmetric acoustic modes localized near the apex, there can also exist a single symmetric acoustic mode. This mode is localizsd in the vicinity of the wedge apex: and its characteristics are close to those of Rayleigh's surface acoustic mode. The phase velocity and the field structure of tbe mode are calculated. The lowest-frequency boundary for the region of its existence is determined.