Question

A string of length 0.4 m and mass ${10}^{-2}$ kg is tightly clampled 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 ∆t. The minimum value of ∆t, which allows constructive interference between succesive 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

Mass per unit length of the string,

$m=\frac{{10}^{-2}}{0.4}=2.5\times {10}^{-2}$ kg/m

$\therefore$ Velocity of wave in the string.

$v=\sqrt{\frac{T}{m}}=\sqrt{\frac{1.6}{2.5\times {10}^{-2}}}$

$v=8m/s$

For constructive interference between successive pulses:

$△t_{min}=\frac{2l}{v}=\frac{\left(2\right)\left(0.4\right)}{8}=0.10s$

(After two reflections, the wave pulse is in same phase as it was produced, since in one reflection its phase changes by $\pi$ and if at this moment next identical pulse is produced, then constructive interference will be obtained.)