Two identical strings X and Z made of the same material have tension TX and TZ in them. If their fundamental frequency are 450 Hz and 300 Hz, respectively, then the ratio TX/TZ is :
Option: 1 2.25
Option: 2 0.44
Option: 3 1.25
Option: 4 1.5

Answers (1)

the velocity of the wave in the string is given by- 

            \nu = \sqrt{\frac{T}{\mu}}

So 

\begin{aligned} &\mathrm{f}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mu}}\\ &\text { For identical string } l \text { and } \mu \text { will be same }\\ &So \ \ \mathrm{f} \propto \sqrt{\mathrm{T}}\\ &\frac{450}{300}=\sqrt{\frac{\mathrm{T}_{\mathrm{x}}}{\mathrm{T}_{\mathrm{y}}}}\\ &\Rightarrow \frac{\mathrm{T}_{\mathrm{x}}}{\mathrm{T}_{\mathrm{y}}}=\frac{9}{4}=2.25 \end{aligned}

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