An experimental study by the ultrasonic method of the phase velocity of longitudinal waves transmitted in liquids contained in tubes. Greatly augmented as well as largely decreased velocities may be obtained in any liquid by suitably adjusting the frequency of the wave or the diameter of the containing tube. This phenomenon, described here at length for the first time, is found to be caused by the selective absorption of energy of the longitudinal wave at certain frequencies, resulting in a velocity-frequency curve analogous to the "anomalous dispersion" curve of optics. In the experiments there is strong indication that the absorbing frequency depends inversely on the diameter of the tube.The fact that the absorption frequency does not depend on the material or length of the tube, or for thin walls on the wall thickness, indicates that it is neither longitudinal nor flexural (lateral) vibrations in the tube walls which causes the phenomenon; and the fact that for any liquid the critical frequency shifts with change of diameter indicates that it is in the column of liquid itself that the energy absorption or transference takes place.These experiments show that it is only at frequencies far removed from absorption i.e., on the regular and flat portions of the velocity-frequency curve some distance from the discontinuity, that the usual theories of sound transmission may safely be applied.
X-Ray Stress Measurement of Three Stress Components of Plane Stress State by the Dual-Axis Inclining Method