A string of length $0.4 m$ and mass ${10}^{-2 kg}$ is rigidly clamped at its ends; the tension in the string being $1.6 N.$ Pulses are produced in the string at time interval $∆t.$ The minimum value of $∆t$ so that successive pulses interfere constructively is

Speed of pulse in the string is

$\mathrm{v}=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{1.6}{{10}^{-2}/0.4}}=8{\mathrm{ms}}^{-1}$

At each reflection from the fixed end, the pulse suffers a phase change of re. Hence after two successive reflections, the pulse will have a phase equal to the phase with which it was produced. If at this moment the next pulse is superposed on the pulse which has suffered two reflections, they will interfere constructively. For this to happen, the minimum time interval between successive pulses is 

$(\mathrm{\Delta }t{)}_{min}=\frac{0.4\mathrm{m}+0.4\mathrm{m}}{8{\mathrm{ms}}^{-1}}=0.1\mathrm{s}$