A string of length `0.4 m` and mass `10^(-2) kg` is clamped at one end . The tension in the string is `1.6 N`. The identical wave pulses are generated at the free end after regular interval of time , `Delta t` . The minimum value of `Delta t` , so that a constructive interference takes place between successive pulses is

Options

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

Answer

B

Explanation

Mass per unit length of the string
`m =(10^(-2))/(0.4)=2.5 xx10^(-2)kg//m`
`:.` Velocity of wave in the string
`v=sqrt((T)/(m))=sqrt((1.6)/(2.5xx10^(-3)))rArr v=8m//s`
For constructive interference between successive pulses
`Delta t_(min)=(2l)/(v)=((2)(0.4))/(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.