Question

check the correctness of the equation V=√E/P , where v is the speed of sound in a medium E and P is the elasticity and density of the medium​

Answer 1

SOLUTION :-

Equation ,

  $\bf V=\sqrt{\dfrac{E}{\rho}$

• V = Speed of sound in a medium

• E = Elasticity of the medium

• $\sf\rho$ = Density of the medium

• Dimensional formula of speed = [ L T⁻¹ ]

• Dimensional formula of elasticity = [ M L⁻¹ T⁻² ]

• Dimensional formula of density = [ M L⁻³ ]

   

   $\longrightarrow\sf [ LT^{-1}] = \sqrt{\dfrac{[ML^{-1}T^{-2}]}{[ML^{-3}]}} \\\\\longrightarrow [ LT^{-1}] = \sqrt{[L^{-1+3}T^{-2}]} \\\\\longrightarrow [ LT^{-1}] = \sqrt{[L^{2}T^{-2}]} \\\\\longrightarrow [ LT^{-1}] = [L^2T^{-2}]^\frac{1}{2}\\\\\longrightarrow\bf [LT^{-1}]= [LT^{-1}]$

∴ Equation is correct

Answer 2

Answer:

hence your equation is correct