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Transvese wave motion

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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

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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 ) ½
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 ...

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