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

Answer

A

Explanation

`y_((x,t))=e^(-(ac^(2)+bt^(2)+2sqrt(ab)xt))`
`=e^(-(sqrt(a)x+sqrt(b)t)^(2))=e^(-(sqrt(b)t+sqrt(a)x)^(2))`
It respresents a transverse wave, where velcoity of wave, `upsilon=(omega)/(K)=(sqrt(b))/(sqrt(a))` in `-ve x-` direction .
Thus, options `(a)` is correct.