Cross-Sectional Correction for Computing Young's Modulus From Longitudinal Resonance Vibrations of Square and Cylindrical Rods

The cross-sectional correction involved in the calculation of Young’s modulus from the longitudinal resonance vibrations of both square and cylindrical bars has been determined by an empirical method. On an order of accuracy of 1 part in 1,000, Bancroft’s correction, developed for longitudinal waves in cylinders of infinite length was found to be satisfactory. For this purpose the thickness of square bars is related to the diameter of cylindrical bars of the same length by 4t(2) = 3d(2). For accuracies of 1 part in 10,000, modifications in Bancroft’s correction must be applied. These modifications take a different form for the square rods than for the cylindrical rods. The relation, 2l=nλ held for both shapes and on the higher order of accuracy, i.e., the cross-sectional correction was the same for the fundamental and overtones on specimens of the same effective length.