1.

A travelling wave is given by `y=(0.8)/((3x^(2)+24xt+48t^(2)+4))` where `x` and `y` are in metres and `t` is in seconds. Find the velocity in `m//s`.

Answer» `y=(0.8)/((3x^(2)+12xt+12t^(2)+4))`
`=(0.8)/(3[x^(2)+4xt+(2t)^(2)]+4)`
`=(0.8)/([4+3(x+2t)^(2)])`
on solving, we get
`x+2t=x+vt`
`v=2 m//s`
Amplitude ua `y_(max):` when `x+2t=0`
therefore, `y_(max)=(0.8)/(4)=0.2m`


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