The disturbance y(x, t) of a wave propagating | vedclass

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(C) The general equation of a wave propagating in the positive $x$-direction is given by $y(x, t) = f(x - vt)$,where $v$ is the wave velocity.At $t =

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(C) The general equation of a wave propagating in the positive $x$-direction is given by $y(x, t) = f(x - vt)$,where $v$ is the wave velocity.At $t = 0$,the equation is $y = f(x) = \frac{1}{1 + x^2}$.At any time $t$,the equation becomes $y = f(x - vt) = \frac{1}{1 + (x - vt)^2}$.Given that at $t = 2 \ s$,the equation is $y = \frac{1}{1 + (x - 1)^2}$.Comparing the two expressions for $t = 2 \ s$:$vt = 1$Since $t = 2 \ s$,we have $v(2) = 1$.Therefore,$v = \frac{1}{2} = 0.5 \ m/s$.

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