Question:
Two identical strings $X$ and $Z$ made of same material have tension $\mathrm{T}_{\mathrm{X}}$ and $\mathrm{T}_{\mathrm{Z}}$ in them. It their fundamental frequencies are $450 \mathrm{~Hz}$ and $300 \mathrm{~Hz}$, respectively, then the ratio $\mathrm{T}_{\mathrm{X}} / \mathrm{T}_{\mathrm{Z}}$ is :
Correct Option: , 3
Solution:
$\mathrm{f}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mu}}$
For identical string $l$ and $\mu$ will be same
$f \propto \sqrt{T}$
$\frac{450}{300}=\sqrt{\frac{\mathrm{T}_{\mathrm{x}}}{\mathrm{T}_{\mathrm{y}}}}$
$\frac{\mathrm{T}_{\mathrm{x}}}{\mathrm{T}_{\mathrm{y}}}=\frac{9}{4}=2.25$
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