Question

The velocity $v$ of sound can be assumed as dependent on density of medium and modulus of elasticity of medium ,so which of the following can be considered as correct formula for calculating velocity of sound,($\rho$=density,$E$=modulus of elasticity)

• A. $v={\rho }^{0.5}\times E^{0.5}$
• B. $v={\rho }^{0.5}\times E^{-0.5}$
• C. $v={\rho }^{-0.5}\times E^{0.5}$
• D. none of the above

Answer 1

The correct option is C $v={\rho }^{-0.5}\times E^{0.5}$

Dimension of velocity $v=\left[L{T}^{-1}\right]$
Dimension of density $\rho =\left[M{L}^{-3}\right]$
Dimension of modulus of Elasticity i.e (stress/strain) $E=\left[M{L}^{-1}{T}^{-2}\right]$
$\frac{E}{\rho }=\frac{\left[M{L}^{-1}{T}^{-2}\right]}{\left[M{L}^{-3}\right]}=\left[L^2{T}^{-2}\right]=v^2$
Therefore option C is correct.