When tension T is applied to a sonometer wire | vedclass

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(C) The fundamental frequency of a sonometer wire is given by the formula: $n = \frac{1}{2\ell} \sqrt{\frac{T}{m}}$,where $T$ is the tension,$\ell$ is

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(C) The fundamental frequency of a sonometer wire is given by the formula: $n = \frac{1}{2\ell} \sqrt{\frac{T}{m}}$,where $T$ is the tension,$\ell$ is the length,and $m$ is the mass per unit length.Initially,$n = \frac{1}{2\ell} \sqrt{\frac{T}{m}}$.When the tension is increased by $8 \ N$,the new tension is $T' = T + 8$. The new frequency is $3n$.So,$3n = \frac{1}{2\ell} \sqrt{\frac{T+8}{m}}$.Dividing the second equation by the first equation:$\frac{3n}{n} = \frac{\frac{1}{2\ell} \sqrt{\frac{T+8}{m}}}{\frac{1}{2\ell} \sqrt{\frac{T}{m}}}$$3 = \sqrt{\frac{T+8}{T}}$Squaring both sides:$9 = \frac{T+8}{T}$$9T = T + 8$$8T = 8$$T = 1 \ N$.

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