Question:
a rope of length L and mass m hangs freely from the ceiling. the velocity of transverse wave as a function of position x along the rope is proportional to
Answer:
Length of the rope = L
Mass of the rope = m
Hence, mass per unit length of the rope = μ = m/L
As the tension on the string balances with the weight of the rope, we can say T = mg
Velocity of the transverse wave = v = √ T / μ = √ mg / (m/L) = √L /g
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