Question

A metal bar with a length of $1.50$ $m$ has density of $6400kg/m^3$. Longitudinal sound waves take $3.90\times {10}^{-4}s$ to travel from one end of the bar to the other. The Young's modulus for this metal is $94.7\times {10}^{x}Pa$. Find x.

Answer 1

Given - $\rho =6400kg/m^3,l=1.50m$,

we have , time taken by wave to travel a distance of $l$ is , ,$t=3.90\times {10}^{-4}s$ ,

by , speed = distance/ time ,

$v=1.50/3.90\times {10}^{-4}=3.85\times {10}^{3}m/s$

now the speed of longitudinal wave in a solid metal bar of density $\rho$ is given by ,

$v=\sqrt{Y/\rho }$ , .....................eq1

where $Y=$ young's modulus of elasticity of metal bar ,

putting the value of $v$ and $\rho$ in eq1 , we get

$3.85\times {10}^3=\sqrt{Y/6400}$ ,

or $(3.85\times {10}^3{)}^2=Y/6400$ ,

or $Y=9.48\times {10}^{10}Pa$