Solution

Given,

Mass of wire (m) = 40 gm = 40 x 10^-3 kg
Length of wire (l) = 80 cm = 80 x 10^-2 m
Fundamental frequency (f) = 60 Hz
speed of wave (v) = ?
Tension in the string (T) = ?

We have , the fundamental frequency in the stretched wire is given by

\(f=\frac v{2l}\)
Or, \(v=f\times2l\)
Or, \(v=f\times2l=60\times2\times80\times10^{-2}=96\) m/s

Again,

\(v=\sqrt{\frac T\mu}\)
Or, \(v=\sqrt{\frac T{m/l}}\)
Or, \(T=v^2x\frac ml=\frac{96^2\times40\times10^{-3}}{80\times10^{-2}}=460.8\) N

Hence, the speed of propagation of the transverse wave in the wire is 96 m/s and the tension in the string is 460.8 N