The shape of a wave propagating in the positive x or negative x-direction is given `y=1/sqrt(1+x^(2))` at t=0 and `y=1/sqrt(2-2x+x^(2))` at t=1s where x and y are in meters the shape the wave disturbance does not change during propagation find the velocity of the wave

Options

A. `1m//s` in positive x direction
B. `1m//s` in negative x direction
C. `1/2 m//s` in positive x direction
D. `1/2 m//s` in negative x direction

Answer

A

Explanation

`y=f(xpmc.t)` is the general wave equation
`at t=0y=f(x) Rightarrowy=1/sqrt(1+x^(2))`
`y=1/sqrt(2-2x+x^(2)) =1/sqrt(1+(x-1)^(2)) = f(x-1) Rightarrow f(x-ct)=f(x-1)at t=1 Rightarrowc=1m//s]`