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A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N m-1 and is stretched by 1.0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring?

A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N m-1 and is stretched by 1.0 cm. If a wave pulse is produced on the string near the wall, how much time will it take to reach the spring?

Grade:10

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
Sol. . l = 40 cm, mass = 10 g ∴ mass per unit length, m = 10 / 40 = 1/4 (g/cm) spring constant K = 160 N/m deflection = x = 1 cm = 0.01 m ⇒ T = kx = 160 * 0.01 = 1.6 N = 16 * 104 dyne Again v = √(T /m) = √(16 *104 /(1/ 4) = 8 * 102 cm/s = 800 cm/s ∴ Time taken by the pulse to reach the spring t = 40/800 = 1/20 = 0/05 sec.

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