A wave is travelling along positive x- direction with velocity `2m//s`. Further, `y(x) equation of the wave pulse at `t=0` is `y=(10)/(2+(2x+4)^(2))` (a) From the given information make complete `y(x, t)` equation. (b) Find `y(x)` equation at `t = 1s`
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A, B, D
(a) Here, coefficient to `x` is `2`. Wave speed is `2m//s`. Therefore, coefficient of `t=v("coefficient of" x)=2xx2=4` units. Further, coefficient of `x` is positive and the wave is travelling along positive x-direction . Hence, coefficient of `t` must be negative. Now, suppose the `y(x, t)` function is `y=(10)/(2+(2x - 4t + alpha)^(2))` Here, `alpha` is a constant. At time `t = 0`, Eq. `(i)` becomes `y=(10)/(2 + (2x + alpha)^(2))` and the function is `y=(10)/(2+(2x + 4)^(2))` Therefore, the value of `alpha` is `4`. Substituting in Eq. `(i)`, we have `y=(10)/(2+ (2x - 4t + 4)^(2))` (b) At `t = 1s` `y=(10)/(2+(2x - 4t + 4)^(2))` or `y=(10)/(2+ 4x^(2))`
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