# Q.15.14  A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45\: Hz$. The mass of the wire is $3.5\times 10^{-2}\: kg$ and its linear mass density is $4.0\times 10^{-2}\: kg\: m^{-1}$. What is   (a) the speed of a transverse wave on the string?

Length of the string is l given by

$\\l=\frac{M}{\mu }\\ l=\frac{3.5\times 10^{-2}}{4\times 10^{-2}}\\ l=0.875m$

Since the wire is vibrating in the fundamental mode

$\\l=\frac{\lambda }{2}\\ \lambda =2l\\ \lambda =2\times 0.875\\ \lambda =1.75m$

Speed of the string (v) is

$\\v=\nu l\\ v=45\times 1.75\\ v=78.75\ ms^{-1}$

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