The transverse displacement `y(x, t)` of a wave on a string is given by `y(x, t)= e ^(-(ax^(2) + bt^(2) + 2sqrt((ab))xt)`. This represents a :

Options

A. Wave moving in -x direction with speed `sqrt((b)/(a))`
B. Standing wave of frequency `sqrt(b)`
C. Standing wave of frequency `(1)/(sqrt(b))`
D. Wave movinb in +x direction with speed `sqrt((a)/(b))`

Answer

A

Explanation

This equation can be written as `y (x, t) = e^(-(sqrt(a)x + sqrt(b)t)^(2))`
Now it is compared with `y(x, t) = e^((kx + omega t)^(2))`
`k = sqrt(a), omega = sqrt(b)`
`upsilon = (omega)/(k) = sqrt((b)/(a))`
Wave moving in negative X-direction