Question

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

Answer 1

Correct Answer - 2
`y(x,t) = e^(-[sqrt(ax)+sqrt(bt)]^(2))`
it is transverse type , `y(x,t) = e^(-(ax + bt)^(2))`
Speed `v = (sqrt(b))/(sqrt(a))`
and wave is moving along `-x` direction.
`y(x,t) = e^(-[sqrt(ax)+sqrt(bt)]^(2))`