The displacement due to a wave moving in the positive x-direction is given by $y = \frac{1}{(1 + x^{2})}$ at time $t=0$ and by $y = \frac{1}{[1+(x-1)^2]}$ at t = 2 seconds, where x and y are in meters. The velocity of the wave in m/s is
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In a wave equation, x and t must be related in the form (x - vt) .
We rewrite the given equations $y = \frac{1}{1 + (x - vt)^2}$
For $t=0,$ this becomes $y = \frac{1}{(1 + x^2)}$ , as given
For $t=2,$ this becomes $y = \frac{1}{\left[1+(x-2v)^2\right]} = \frac{1}{\left[1+(x-1)^2\right]}$
⇒ ⇒ 2v = 1 or $\mathbf{v} = 0.5 \mathrm{m}/\mathrm{s}$ .
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