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A string of length 0.4 m and mass 10^(-2...

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

A

0.05 s

B

0.10 s

C

0.20 s

D

0.40 s

Text Solution

Verified by Experts

The correct Answer is:
B
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.
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Knowledge Check

  • A string of length 0.4 m and mass 10^(-2)kg is tightly clamped at its ends. The tension in the dtring is 1.6 N . Idential wave pulse are produced at one end at equal intervals of time, Deltat . The minimum value of Deltat which allows constructive inetrference successive pulse is

    A
    (a) `0.04s`
    B
    (b)`0.10s`
    C
    ( c ) `0.20s`
    D
    (d) `0.40 s`

  • A string of length 0.4 m and mass 10^(-2) kg is clamped at its ends. The tension in the string is 1.6 N. When a pulse travels along the string the shape of the string is found to be the same at times t and t+trianglet . The value trianglet is

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    B
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    D
    0.4s

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