Question

A 500-g metal wire has a length of 50 cm and is under tension of 80 N. (a) What is the speed of a transverse wave in the wire? (b) If the wire is cut in half, what will be the speed of the wave?

Answer 1

Step-by-step 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 :

`v=\sqrt{(T)/(M)}`

M is the mass per unit length or M = m/l

`v=\sqrt{(T.l)/(m)}`

`v=\sqrt{(80\ N* 0.5\ m)/(0.5\ kg)}`

v = 8.94 m/s

(b) If the wire is cut in half, so l = l/2

`v=\sqrt{(T.l)/(2m)}`

`v=\sqrt{(80\ N* 0.5\ m)/(2* 0.5\ kg)}`

v = 6.32 m/s

Hence, this is the required solution.