Dispersion of Ultrasonic Pulse Velocity in Cylindrical Rods

Abstract

The velocities of pulsed longitudinal and shear waves in cylindrical rods of aluminum alloy, brass, copper, and steel were measured by using both the pulse echo and pulse transmission methods. It is found that for pulsed longitudinal waves the measured velocity not only depends upon the elastic constants of the medium but also on the ratio between the radius a of the rod and the wavelength λ. When this ratio a/λ is very small the measured velocity approximates the Young's modulus velocity (E/ρ)12. For large values of a/λ the measured velocity approaches the bulk velocity [(l+2μ/ρ]12 where l and μ are the Lamé elastic constants. Where a/λ is in the vicinity of unity, the velocity drops and seems to approach Rayleigh surface wave velocity. This velocity dispersion effect was not observable when pulsed shear wave was used instead of longitudinal waves. A qualitative explanation for the increase of the measured pulse velocity when a/λ is large based on the equations of motion was given.