What is the fractional change in the tension necessary in a sonometer of fixed length to produce a n

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What is the fractional change in the tension necessary in a sonometer of fixed length to produce a note one octave lower (half of original frequency) than before

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Sol. $f = \frac{nv}{2L}$ length fixed. v∝$\sqrt{T}$$f \propto \sqrt{T}$$f' = \frac{f}{2}$$\frac{f}{\sqrt{T}} = \frac{f'}{\sqrt{T'}}$$T' = \frac{T}{4}$Fractional change$= \frac{\Delta T}{T} = \frac{T - T/4}{T} = \frac{3}{4}$

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