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 in equal intervals of times `Delta`t. the minimum value of `Delta`t, which allows constructive interference between successive pulses , is :

Options

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

Answer

D

Explanation

In a string velocity of wave pulse is v = `sqrt((T)/(m))`
` v = sqrt(((1.6)/(10^(-2)))/(0.4)) = `8 m/s.
When the pulse is reflected at the end it suffers a phase chase of `pi`. Again with reflection at other end it suffers a phase change of `pi`. so the original pulse is obtianed after two reflections . If wave is produced at that instant them two waves interfere constructively.
`therefore` Minimum time for the same is t `= (l + l)/(v)`
`= (0.4 + 0.4)/(8) = (1)/(10) = 0.1 ` s.
Correct choice is (d).