Question

A 30 m steel wire and a 20 m copper wire ,both with 1mm diameters,are connected end to end and stretched to a tension of 150N.How long does it take a transverse wave to travel the entire length of the two wires ?

Answer 1

Speed of transverse wave in wire can be given as
$$\begin{gathered} v=\sqrt{\frac{T}{\mu }} \\ \mu islineardensityandisequalto\mu =\frac{m}{L} \\ Density\rho =\frac{Mass}{Volume}=\frac{m}{\pi r^{2}L} \\ \rho =\frac{\mu }{\pi r^2} \\ v=\sqrt{\frac{T}{\rho \pi r^2}} \end{gathered}$$
So, speed of transverse wave in steel wire is
v = 154.063 m/s (Density of steel = 8050 kg/m³ )
Therefore time taken by wave to travel through 30 m steel wire = 0.194 s

Speed of transverse wave in copper wire is
v = 146.03 m/s (Density of copper = 8960 kg/m³)
Therefore time taken by wave to travel through 20 m steel wire = 0.14 s


Therefore total time taken by wave to travel entire length of two wire is = 0.194 s + 0.14 s = 0.33 s