A travelling wave travelled in string in...

A travelling wave travelled in string in `+x` direction with `2 cm//s`, particle at `x = 0` oscillates according to equation y (in mm) `= 2 sin (pi t+pi//3)`. What will be the slope of the wave at `x = 3cm` and `t = 1s` ?

`-sqrt(3)pi//20`

`-sqrt(3)pi//2`

`tan^(-1)(-sqrt(3)pi//2)`

`-sqrt(3)pi`

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The correct Answer is:

Equation of wave can be given as
`y=0.2sin(pit-(pi)/(2)x+(pi)/(3))`
slope `=(dely)/(delx)=-0.1xxpicos(pit-(pi)/(2)x+(pi)/(3))`
`(dely)/(delx)=-(pi)/(10)cos[pi-(3pi)/(2)+(pi)/(3)]`
`=-(sqrt(3))/(20)`

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