The amplitude of wave disturbance propagating in the positive x-direction is given by   $y=\frac{1}{1+{\left(x\right)}^2}$ at time t = 0 and $y=\frac{1}{1+{\left(x-2\right)}^2}$  at t = 1s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be_______ m/s.

<p>The equation of wave at any time t will be<span class="mathml" contenteditable="false"> <math> <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mi>x</mi> <mo>? </mo> <mi>v</mi> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>, </mo> </mrow> </math> </span> &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816094033"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;so v * 1 = 2 -&gt; v = 2m/s</p>

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