A sonometer wire resonates with a given tunin | vedclass

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(A) The frequency of vibration of a sonometer wire is given by $n = \frac{p}{2l} \sqrt{\frac{T}{\mu}}$,where $p$ is the number of loops (antinodes),$l

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$25$

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(A) The frequency of vibration of a sonometer wire is given by $n = \frac{p}{2l} \sqrt{\frac{T}{\mu}}$,where $p$ is the number of loops (antinodes),$l$ is the length,$T$ is the tension,and $\mu$ is the mass per unit length.In the first case,$p_1 = 5$ and $T_1 = 9g$. Thus,$n = \frac{5}{2l} \sqrt{\frac{9g}{\mu}}$.In the second case,$p_2 = 3$ and $T_2 = Mg$. Thus,$n = \frac{3}{2l} \sqrt{\frac{Mg}{\mu}}$.Since the tuning fork is the same,the frequency $n$ remains constant. Equating the two expressions:$\frac{5}{2l} \sqrt{\frac{9g}{\mu}} = \frac{3}{2l} \sqrt{\frac{Mg}{\mu}}$Squaring both sides:$25 	imes 9g = 9 	imes Mg$$225g = 9Mg$$M = \frac{225}{9} = 25 \ kg$.

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