Question

The Young's modulus and density of a certain kind of stainless steel are 180 GPa and 8 g cm 3 − respectively.
(a) Estimate the speed of sound wave in the steel.

Answer 1

"The value of v for waves traveling along the length of a bar or rod is defined by the Young's modulus and the density:
\[v=\Bigg( \frac{Y}{\rho}\Bigg)^{1/2}\]"

p.210 Vibrations and Waves, A.P. French.

The derivation for it is on p. 172, from

\[ \frac{\partial^2 \xi}{\partial x^2} = \frac{\rho}{Y} \frac{\partial^2 \xi}{\partial t^2} = \frac{1}{v^2}\frac{\partial ^2 \xi}{\partial t^2}\]

\[v^2 = \frac{Y}{\rho}\]
Where xi is longitudinal displacement from equilibrium - it's just the form of the wave equation applied to weird stress forces.

Answer 2

http://books.google.com/books?id=RqE26vDmd5wC&printsec=frontcover&dq=vibrations+and+waves&hl=en&sa=X&ei=m8iSUt2bAoWVrAHB2IGoDA&ved=0CB8Q6AEwAA#v=snippet&q=%22observed%20speeds%20of%20sounds%22&f=false

Answer 3

thanks!!