Explanation:
It is given that,
Mass of the metal wire, m = 500 g = 0.5 kg
Tension in the wire, T = 80 N
Length of wire, l = 50 cm = 0.5 m
(a) The speed of the transverse wave is given by :
[tex]v=\sqrt{\dfrac{T}{M}}[/tex]
M is the mass per unit length or M = m/l
[tex]v=\sqrt{\dfrac{T.l}{m}}[/tex]
[tex]v=\sqrt{\dfrac{80\ N\times 0.5\ m}{0.5\ kg}}[/tex]
v = 8.94 m/s
(b) If the wire is cut in half, so l = l/2
[tex]v=\sqrt{\dfrac{T.l}{2m}}[/tex]
[tex]v=\sqrt{\dfrac{80\ N\times 0.5\ m}{2\times 0.5\ kg}}[/tex]
v = 6.32 m/s
Hence, this is the required solution.
