Question

At t=0, transverse pulse in a wire is described by the function
`y=(6)/(x^(2)+3)`
where x and y are in metres. Write the function `y(x,t)` that describe this plus if it is travelling in the positive x-direction with a speed of `4.50 m//s`.

Answer 1

At `t=0`, the wave pulse looks like a bump centred at `x=0`. as time goes on, the wave function will be function of `t` as well as `x`. the point about which the bump is centre will be `X_(0)=4.5t`.
we obtain a function of the same shape by writing
`(y(x,t)=6(x-4.5t)^(2)+3)`
Note that for `y` to stay constant as `t` increase, `x` must increase by `4.5 t`, as it describes the wave movie at `4.5 m//s`.