Physics

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)


ANSWER

$$v = \rho^{-0.5} \times E^{0.5}$$


SOLUTION
Dimension of velocity $$v= [LT^{-1}]$$
Dimension of density $$\rho=[ML^{-3}]$$
Dimension of modulus of Elasticity i.e (stress/strain)   $$E=[ML^{-1}T^{-2}]$$
$$\frac{E}{\rho}=\frac{[ML^{-1}T^{-2}]}{[ML^{-3}]}=[L^2T^{-2}]=v^2$$
Therefore option C is correct. 
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Single Correct Medium Published on 18th 08, 2020
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