Question

a) The magnitude of the speed of longitudinal waves in a rod of a certain metal has been measured in 3550 m/s; find the Young’s modulus of the rod if the density of the material it is made of is r=7850 kg/m3?

Answer 1

The speed of longitudinal waves is given as follows (see http://spiff.rit.edu/classes/phys283/lectures/long/long.html):

$$v = \sqrt{\dfrac{Y}{\rho}}$$

where $Y$ is the Young's module and $\rho =7580kg/m^3$ is the density of the rod. Substituting $v = 3550m/s$, obtain:

$$Y = \rho v^2\\ Y = 7580kg/m^3\cdot (3550m/s)^2 \approx 2.69\times 10^7Pa$$

Answer. $2.69\times 10^7Pa$.