Answer to Question #243840 in Physics for cam

Question #243840

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?


1
Expert's answer
2021-09-29T17:51:04-0400

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


v=Yρv = \sqrt{\dfrac{Y}{\rho}}

where YY is the Young's module and ρ=7580kg/m3\rho =7580kg/m^3 is the density of the rod. Substituting v=3550m/sv = 3550m/s, obtain:


Y=ρv2Y=7580kg/m3(3550m/s)22.69×107PaY = \rho v^2\\ Y = 7580kg/m^3\cdot (3550m/s)^2 \approx 2.69\times 10^7Pa

Answer. 2.69×107Pa2.69\times 10^7Pa.


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