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(D) The tension $T$ in the wire is equal to the weight of the hanging mass,$T = Mg = 9 	imes 9.8 = 88.2 \, N$.The linear mass density $\mu$ is $\mu =

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None of these

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(D) The tension $T$ in the wire is equal to the weight of the hanging mass,$T = Mg = 9 	imes 9.8 = 88.2 \, N$.The linear mass density $\mu$ is $\mu = \frac{m}{l} = \frac{12 	imes 10^{-3} \, kg}{1.5 \, m} = 8 	imes 10^{-3} \, kg/m$.The velocity of the transverse wave is $v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{88.2}{8 	imes 10^{-3}}} = \sqrt{11025} = 105 \, m/s$.For vibration in $p=3$ loops,the frequency $f$ is given by $f = \frac{p v}{2l}$.Substituting the values,$f = \frac{3 	imes 105}{2 	imes 1.5} = \frac{315}{3} = 105 \, Hz$.Since $105 \, Hz$ is not among the options,the correct choice is $D$.

The length of the wire shown in the figure between the pulleys is $1.5 \, m$ and its mass is $12.0 \, g$. The frequency of vibration with which the wire vibrates in three loops,forming an antinode at the midpoint of the wire,is: (Given $g = 9.8 \, m/s^2$)

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