The fundamental frequency of a sonometer wire is increases by $6\, Hz$ if its tension is increased by $44\%$, keeping the length constant. The frequency of the wire is ...... $Hz$
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By $n=\frac{1}{2 \ell} \sqrt{\frac{T}{m}}$
$\mathrm{n} \propto \sqrt{\mathrm{T}}$
$\frac{\mathrm{n}}{\mathrm{n}+6}=\sqrt{\frac{100}{144}}=\frac{10}{12}$
$\Rightarrow 12 \mathrm{n}=10 \mathrm{n}+60$
$\mathrm{n}=30 \mathrm{Hz}$
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