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(C) Given:Frequency of fundamental mode,$n = 50 \, Hz$Mass of the wire,$M = 30 \, g = 30 	imes 10^{-3} \, kg$Linear mass density,$\mu = 4 	imes 10^{

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$75$

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(C) Given:Frequency of fundamental mode,$n = 50 \, Hz$Mass of the wire,$M = 30 \, g = 30 	imes 10^{-3} \, kg$Linear mass density,$\mu = 4 	imes 10^{-2} \, kg/m$First,we find the length of the wire $(L)$:Since $\mu = M/L$,we have $L = M/\mu$$L = (30 	imes 10^{-3} \, kg) / (4 	imes 10^{-2} \, kg/m) = 0.75 \, m$For the fundamental mode of vibration in a string fixed at both ends:$L = \lambda / 2$$\lambda = 2L = 2 	imes 0.75 \, m = 1.5 \, m$The speed of the transverse wave $(v)$ is given by:$v = n \lambda$$v = 50 \, Hz 	imes 1.5 \, m = 75 \, m/s$

$A$ wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $50 \, Hz$. The mass of the wire is $30 \, g$ and its linear density is $4 \times 10^{-2} \, kg/m$. The speed of the transverse wave on the string is ...... $m/s$.

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