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Question
A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?
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Solution 1
Mass of the string, M = 2.50 kg
Tension in the string, T = 200 N
Length of the string, l = 20.0 m
Mass per unit length, `mu = M/l = 2.50/20 = 0.125 "kg m"^(-1)`
The velocity (v) of the transverse wave in the string is given by the relation:
`v = sqrt(T/mu)`
`= sqrt(200/0.125) = sqrt(1600)` = 40 m/s
∴Time taken by the disturbance to reach the other end, `t = l/v = 20/40 = 0.50 s`
Solution 2
Tension,T = 200 N
Length l = 20.0 m , Mass M = 2.50 kg
Mass per unit length, mu = `2.50/20.0 kg m^(-1) = 0.125 kg m^(-1)`
Wave velocity, `v = sqrt(T/mu) = sqrt(200 N)/(0.125 kg m^(-1))`
or `v = sqrt(1600) ms^(-1) = 40 ms^(-1)`
`Time t = l/v = 20.0/40 s = 1/2 s = 0.5 s`
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