If the wave speed on a stretched string depends on the tension \( F \) and linear mass density \( \mu \) as \( v \propto F^{a} / \mu^{b} \), use dimensional analysis to show that \( a=1 / 2 \) and \( b=1 / 2 \).
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- Wave speed \( v \) has dimensions of \([L][T]^{-1}\). - Tension \( F \) has dimensions of \([M][L][T]^{-2}\). - Linear mass density \( \mu \) has dimensions of \([M][L]^{-1}\). Show moreā¦
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Assuming that the wave speed on a stretched string depends on the tension $F$ and linear mass density $\mu$ as $v \propto F^{a} / \mu^{b}$, use dimensional analysis to show that $a=\frac{1}{2}$ and $b=\frac{1}{2}$.
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