Laplace corrected Newton's calculation for the velocity of sound. Laplace said that speed of sound in a solid medium depends upon the coefficient of elasticity of the medium under adiabatic conditons (E) and the density of the medium `(rho)` . Prove that `v=ksqrt((E)/(rho))`

Explanation

`[E]=(F//A)/(((DeltaV)/V)=ML^(-1)T^(-2))`
`[rho]=ML^(-3)`
Let
`v=k(E)^(a)(rho)^(b), [k rarr "Proposnality constant"]`
`LT^(-1)=(mL^(-1)T^(-2))^(a)(ML^(-3))^(b)`
`a+b=0,-a-3b=a,-2a=-1` ltbr. `a=(1)/(2),b=-(1)/(2)` ltbr. So `" " v=kE^(1//2) rho^(-1//2)=ksqrt((E)/(rho))`