On the Propagation of High Frequency Compressional Waves in Isotropic Cylinders

The possible modes of propagation of compressional waves in solid cylindrical rods are described by the solutions of the `frequency equation'. It has been found possible to solve this equation at frequencies near 10 Mc/s by a graphical method which is readily applicable. Using this method the variation of phase velocity ν p with frequency has been evaluated for the most important modes of propagation, namely those having phase velocities near to that in an unbounded medium, ν 1 . It is shown that in the vicinity of ν p =ν 1 the variation of phase velocity with frequency is characterized by a series of `plateau' regions over which ν p is approximately constant, these regions being separated by `steps' through which ν p changes rapidly with frequency. Consideration of the displacement amplitudes shows that the mode with ν p nearest to ν 1 has, in general, a pressure variation across the radius which is most likely to be excited experimentally under conditions described in a previous paper by the authors.