The displacement equation of a traveling wave pulse, moving along X axis is given by `y=(8)/((4+x^(2))^(2)) at t=0 and y=(8)/((x^(2)-10x+29))` What is the speed and direction of the prelse?

Explanation

The given equation corresponding to t= 1 can be rewritten as, `y=(8)/((x^(2)-10x+25)+4)=(8)/(4+(x-5)^(2))=(8)/(4+[x-5(1)]^(2))`
since the displacement equation of a wave is necessarily a function of (x + v), so the above equation can be rewritten `y=(8)/(4+[x-5(1)^(2)])`
Evidently factor (x-5t) reveals that the wave is moving along positive X-axis, and its speed is 5 units.