Answer
The mass of the wire is 0.337 kg
Work Step by Step
We can find the speed of the transverse wave.
$v = \frac{d}{t}$
$v = \frac{3.80~m}{0.0492~s}$
$v = 77.24~m/s$
The tension in the wire will be equal to the weight of the object of mass $m_o = 54.0~kg$. We can find the mass $m_w$ of the wire.
$v = \sqrt{\frac{F_T}{\mu}}$
$\mu = \frac{F_T}{v^2}$
$\frac{m_w}{L} = \frac{m_o~g}{v^2}$
$m_w = \frac{m_o~g~L}{v^2}$
$m_w = \frac{(54.0~kg)(9.80~m/s^2)(3.80~m)}{(77.24~m/s)^2}$
$m_w = 0.337~kg$
The mass of the wire is 0.337 kg
