Physics

# Velocity '$V$'  of a wave is directly proportional to modulus of elasticity '$E$' and density '$d$' of a medium. The expression of '$V$' using dimensional analysis is:

$V=\sqrt { \dfrac { E }{ d } }$

##### SOLUTION

$V\propto E^{\alpha } d^{\beta }$

$M^{0}L^{1}T^{-1}=(M^{1}L^{-1}T^{-2})^{\alpha}(ML^{-3})^{\beta }$
$M^{0}L^{1}T^{-1}=M^{\alpha+\beta }L^{-\alpha -3\beta }T^{-2d}$
$\Rightarrow \alpha+\beta =0$
$\Rightarrow-\alpha-3\beta =1$

$-2\alpha=-1$ $\Rightarrow \alpha =\frac{1}{2},\beta =-\frac{1}{2}$
$\Rightarrow v=\sqrt{\dfrac{E}{d}}$

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Single Correct Medium Published on 18th 08, 2020
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