Question

A string of length 0.4 m and mass ${10}^{-2}$ 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 $\Delta t$. The minimum value of $\Delta t$ which allows constructive interference between successive pulses is

• A. 0.05 s
• B. 0.10 s
• C. 0.20 s
• D. 0.40 s

Answer 1

The correct option is B

0.10 s

For string, $\frac{Mass}{Lenght}=m=\frac{{10}^{-2}}{0.4}=2.5\times {10}^{-2}kg/m$

$\therefore Velocityv=\sqrt{\frac{T}{m}}=\sqrt{\frac{16}{2.5\times {10}^{-2}}}=8m/s$

For constructive interference between successive pulses.

$△t_{min}=\frac{2l}{v}=\frac{2\left(0.4\right)}{8}=0.1sec$

( After two reflections, the wave pulse is in same

phase as it was produced since in one reflection

it's phase changes by $\pi$ and If at this moment

next identical pulse is produced, then

constructive interference will be obtained. )