# Transvese wave motion

A mass M hangs vertically on a rope of mass m and length L.

a) Show that the time for a transverse wave to travel the length of the rope is:

t= 2(L/mg)^1/2[(M+m)^1/2-M^1/2]

b) Show that this reduces to t=2(L/g)^1/2 when M=0

c) Show that for m<M part a) reduces to t=(ml/Mg)^1/2

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:32 am ad1c9bdddfhttps://brainmass.com/physics/velocity/transverse-wave-motion-4890

#### Solution Preview

Formatting is preserved in the file attached.

A mass M hangs vertically on a rope of mass m and length L.

a) show that the time for a transverse wave to travel the length of the rope is:

t= 2(L/mg)^1/2[(M+m)^1/2-M^1/2]

Velocity of wave = (T/ Mu ) Â½

Where T is the tension and Mu is the mass per unit length = m/ L

Tension in the rope at the top= Mg

Tension in the rope at the bottom= (M+m) g (since the weight of the rope contributes to the ...

#### Solution Summary

This solution provides poofs regarding time for a transverse wave to travel the length of the rope.