A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

Question

Philoid · Accepted Answer

Given:

Mass of the string, M = 2.50 Kg

Tension in the string, T = 200 N

Length of the string, L = 20 m

Mass per unit length, m = M/L

⇒ m = 2.50 Kg/ 20m

⇒ m = 0.125 Kgm^-1

The velocity, V of the transverse wave in the string is given by as,

V = (T/m)^-2 …(1)

Where,

T = tension in the string

m = mass per unit length

By putting the given data in equation (1), we get,

⇒ v = 40 ms^-1

Time, t taken for the wave to get to the other end can be given by,

t = L/V …(2)

Where,

L = length of the string

V = velocity of wave

Using equation (2),

t = 20m/ 40 ms^-1

t = 0.5 s