i) A long rope with mass m = 10 kg is suspended from the ceiling and hangs verti

Question

i) A long rope with mass m = 10 kg is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope and the pulse travels up the rope.
(a) Does the speed of the wave pulse change as it moves up the rope, and if so, does it increase or decrease?
(b) A man of mass 80 kg starts to climb the rope. Given that the wave speed at the top beforehand was 30 ms1, what will the wave speed at the top be after the man starts climbing?
ii). For the situation described above, calculate the time it would take a wave pulse to propagate from the bottom of the rope to the top, (a) before and (b) after the man has started climbing (for the time after he has started climbing, assume he is at the bottom of the rope). For simplicity of calculation, use g = 10 ms2.

Explanation / Answer

Here ,

as the speed of wave is given as

v = sqrt(T/(m/L))

as thr tension in the rope will increase as we go higher in the rope.

the speed of the wave pulse increase up the wave.

b)

let the speed after man start climbing is v2

initial speed , v1 = 30 m/s

v1/v2 = sqrt(T1/T2)

30/v2 = sqrt((10 * 9.8)/(10 + 80) * 9.8)

v2 = 90 m/s

the speed of wave is 90 m/s

c)

before

let the length is L

time before = L/30

time after = L/90

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