The speed of sound in a solid is given by the formula: v= E Where… - Vidyadip

Question

The speed of sound in a solid is given by the formula: $\text{v}=\sqrt{\frac{\text{E}}{\rho}}$ Where, E is coefficient of elasticity and pis density of given solid. Check the relation by method of dimensional analysis.

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Answer

In the given relation dimensions of LHS terms v are $\left[\mathrm{LT}^{-1}\right]$ Dimensional formula for $E$ and $p$ are $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right)$ and $\left[\mathrm{ML}^{-3}\right]$ Dimesnsions of RHS $=\sqrt{\frac{\mathrm{ML}^{-1} \mathrm{~T}^{-1}}{\mathrm{ML}^{-3}}}=\sqrt{\mathrm{L}^2 \mathrm{~T}^{-2}}=\left[\mathrm{LT}^{-1}\right]$ As dimensions of LHS and RHS of the equation are same Hence the equation is dimensionally correct.

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