A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at the lowest end. It starts moving up the string. The time taken to reach the support is: (take g=10 m/s²)

The tension in a string of linear mass density λ as a function of length x measured from the free end is Tx = λxg. The velocity of wave when it is at a position x is vx = √(Tx/λ) = √(xg). dx/dt = √(xg) T = ∫0L dx/√(xg) = 2√(L/g) = 2√(20/10) = 2√2s