A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. (a) Find the speed of transverse wave in the rope at a point 0.5 m distant from the lower end, (b) Calculate the time taken by a transverse wave to travel the full length of the rope (g = 9.8 m/s2)
2.21 m/s & 1 sec
(a) As the string has mass and it is suspended vertically, tension in it will be different at different points. For a point at a distance x from the free end, tension will be due to the weight of the string below it. So if M is the mass of string of length L, the mass of length x of the string will be (M/L)x.
Here x = 0.5 m
(b) From part (a) it is clear that the tension and so the velocity of the wave is different at different points. So if at point x the wave travels a distancedx in time dt,
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