Determining the Young's modulus on solids from the measurement of the speed of sound by the time-of-flight method

The Young's modulus $\left(Y\right)$ is a quantity related to the linear elasticity of a material. The most common techniques for determining the Young's modulus involve the measurement of the deformation of a flexed beam, or the measurement of the deformation of a wire submitted to a tractive effort. Another known technique consists of measuring the speed of sound $\left(c\right)$ on a thin rod, which is related to $Y$ by the expression $Y=\rho c^2$, where $\rho$ is the density of the material under study. Thus, by knowing $\rho$, $Y$ can be determined through the measurement of $c$. In this work we carried out collision experiments to generate compression pulses in thin solid rods and employ the time-of-flight method to measure the speed of sound in different materials. The flight time is the time needed for the pulse to cover the distance between two points of the rod. This time was measured by means of an assembly which utilizes two mechanical contact switches associated with an electric circuit comprising an electronic counter and a crystal oscillator. The experiments were conducted using different materials (stainless steel, brass and wood) and calculated the respective Young's modules and their statistical deviations.

Key words:
Young's modulus; elasticity; compression pulse; flight time; digital counter