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  4. What is the fractional change in tension necessary in a sonometer of fixed length to produce a note one octave lower than before?

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Q. What is the fractional change in tension necessary in a sonometer of fixed length to produce a note one octave lower than before?

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Solution:

$n =\frac{1}{2l} \sqrt{\frac{ T'}{ m }}$
$\frac{ n }{2}=\frac{1}{2l} \sqrt{\frac{ T'}{ m }}$
by (i) $\&$ (ii)
$\frac{ T'}{ T }=\frac{1}{4}$
Subtract both side from 1
$-1-\frac{T'}{T}=1-\frac{1}{4}$
$\frac{ T - T'}{ T }=\frac{3}{4}$