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 as :
Wave moving along + x-axis with a speed `sqrt((a)/(b))`
Wave moving along - x-axis with speed `sqrt((b)/(a))`
Standing wave of frequency `sqrt (b)`
Standing wave of frequency `(1)/(sqrt (b))`

Options

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

Answer

D

Explanation

`y(x_(1)t)=e^(-[sqrt(ax)+sqrt(bt)]^(2))`
`v = omega//K=(sqrt(b))/(sqrt(a))` in `-ve` x direction