Measuring the Young’s modulus of reeds from American reed organs.

Abstract

A method of wave coefficients has been used to measure the Young’s modulus of brass reeds from American reed organs. Although for some purposes these reeds can be approximated as uniform cantilever beams, their cross sections are sufficiently nonuniform that simple methods such as measuring beam displacement for a known applied force or using resonant frequencies of transverse and torsional modes of vibration are not sufficient to obtain accurate results. In the wave coefficient method [Y. Liao and V. Wells, J. Sound Vibr. 295, 165–193 (2006)] a wave number is found that forces data at all measurement points to conform to the general forced-vibration solution for a beam, implying that they have the same wave coefficients. This method also assumes a uniform cross section but does not require measurements along the entire length of the beam and was applied only to the most uniform sections of the reeds. Three reeds of the same frequency were selected, with cross sections of varying uniformity. The resulting measurements of the Young’s modulus seemed consistent with expected values for brass. For one reed with nearly uniform cross section the wave coefficient method was in good agreement with the simpler methods.