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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` ?

A

`-sqrt(3)pi//2`

B

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

C

`-sqrt(3)pi//20`

D

`-sqrt(3)pi`

Text Solution

Verified by Experts

The correct Answer is:
C
A travelling wave…………..
`y = 2sin pi(t-(x)/(2)+(1)/(3))`
`(dy)/(dx) = 2cos (pi t - (pi x)/(2)+(pi)/(3))xx(-(pi)/(2))`
Equation of wave can be given as
`y = 0.2 sin (pi t - (pi)/(2)x +(pi)/(3))`
Slope3 `= (del y)/(del x) = -0.1xxpi cos (pi t-(pi)/(2)x +(pi)/(3))`
`(del y)/(del x)= -(pi)/(10)cos [pi - (3pi)/(2)+(pi)/(3)]= - (sqrt(3)pi)/(20)`
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