A string of length 0.4 m and mass ${10}^{-2}\mathrm{kg}$ is tightly clamped at its ends. The tension in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time $\mathrm{\Delta t}$. The minimum value of $\mathrm{\Delta t}$ which allows constructive interference between successive pulses is 

For string,  $\frac{\text{Mass}}{\text{Length}}=\mathrm{m}=\frac{{10}^{-2}}{0.4}=2.5\times {10}^{-2}\mathrm{kg}/\mathrm{m}$
$\therefore$ Velocity  $\mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mathrm{m}}}=\sqrt{\frac{16}{2.5\times {10}^{-2}}}=8\mathrm{m}/\mathrm{s}$
For constructive interference between successive pulses.
       ${\mathrm{\Delta t}}_{\min }=\frac{2\mathrm{l}}{\mathrm{v}}=\frac{2(0.4)}{8}=0.1\sec$
(After two reflections, the wave pulse is in same phase as it was produced since in one reflection it’s phase changes by $\mathrm{\pi }$, and If at this moment next identical pulse is produced, then  constructive interference will be obtained.