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A pulse is started at a time t = 0 along...

A pulse is started at a time `t = 0` along the `+x` directions an a long, taut string. The shaot of the puise at `t = 0` is given by funcation `y` with
`y = {{:((x)/(4)+1fo r-4ltxle0),(-x+1fo r0ltxlt1),("0 otherwise"):}`
here `y` and `x` are in centimeters. The linear mass density of the string is `50 g//m` and it is under a tension of `5N`,
the shape of the string is drawn at `t = 0` and lthe area of the pulse elclosed by the string and the `x-`string is measured. It will be equal to `

A

`2 cm^(2)`

B

`2.5 cm^(2)`

C

`4 cm^(2)`

D

`5 cm^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Shape of the pulse at `t = 0`
That is a triangular pulse Area of the pulse
`= (1)/(2)[(4 xx 1) + (1 xx 1)]`
`= (5)/(2) cm^(2)`
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Knowledge Check

  • A pulse is started at a time t = 0 along the +x directions an a long, taut string. The shaot of the puise at t = 0 is given by funcation y with y = {{:((x)/(4)+1fo r-4ltxle0),(-x+1fo r0ltxlt1),("0 otherwise"):} here y and x are in centimeters. The linear mass density of the string is 50 g//m and it is under a tension of 5N , The vertical displacement of the particle of the string at x = 7 cm and t = 0.01 s will be

    A
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    B
    `0.5 cm`
    C
    `0.25 cm`
    D
    zero

  • A pulse is started at a time t = 0 along the +x directions an a long, taut string. The shaot of the puise at t = 0 is given by funcation y with y = {{:((x)/(4)+1fo r-4ltxle0),(-x+1fo r0ltxlt1),("0 otherwise"):} here y and x are in centimeters. The linear mass density of the string is 50 g//m and it is under a tension of 5N , The vertical displacement of the particle of the string at x = 7 cm and t = 0.01 s will be

    A
    `0.75 cm`
    B
    `0.5 cm`
    C
    `0.25 cm`
    D
    zero

  • A pulse is started at a time t = 0 along the +x directions an a long, taut string. The shaot of the puise at t = 0 is given by funcation y with y = {{:((x)/(4)+1fo r-4ltxle0),(-x+1fo r0ltxlt1),("0 otherwise"):} here y and x are in centimeters. The linear mass density of the string is 50 g//m and it is under a tension of 5N , The transverse velocity of the particle at x = 13 cm and t = 0.015 s will be

    A
    `-250 cm//s`
    B
    `-500 cm//s`
    C
    `500 cm//s`
    D
    `-1000 cm//s`