A string of length 25 ~cm and mass 10⁻³ ~kg is clamped at its ends. The tension in the string is 2.5 ~N . The identical wave pulses are generated at one end and at regular interval of time, t . The minimum value of t , so that a constructive interference takes place between successive pulses is

Step-by-step solution

The linear mass density of the string is given by = M L = 10⁻³ kg 0.25 m = 4 10⁻³ kg/m . The speed of the wave v in the string is v = T = 2.5 4 10⁻³ = 2500 4 = 625 = 25 m/s . The time taken for a pulse to travel from one end to the other is t = L v = 0.25 m 25 m/s = 0.01 s = 10 ms . For constructive interference between successive pulses, the pulses must return to the starting point in phase. A pulse travels to the other end (10 ms), reflects (phase change of ), and returns to the starting end (another 10 ms). The