Q: 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 ∆t. the minimum value of ∆t which allow constructive interference between successive pulses, is

(a) 0.05 s

(b) 0.10 s

(c) 0.20 s

(d) 0.40 s

Ans: (b)

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

Velocity of wave in a string is

$\large v= \sqrt{\frac{T}{\mu}}$

$\large v= \sqrt{\frac{16}{2.5 \times 10^{-2}}} = 8 m/s$

For constructive interference between successive pulses

$\large \Delta t = \frac{2l}{v} = \frac{2 \times 0.4}{8}$

= 0.10 sec