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. wave moving `-x` direction with speed `sqrt((b)/(a))`
C. standing wave of frequency `sqrtb`
D. standing wave of frequency `(1)/(sqrtb)`

Answer

B

Explanation

`y (x,t) = e^(-(ax^(2) + bt^(2) + 2 sqrt(ab)xt))`
`= e^(-(sqrt(ax) + sqrt(bt))^(2))`
Comparing this with the standard equation,
y (x,t) `= f (kx + omega t)`
We find that the wave is travelling in the -ve direction of the X-axis, because there is a +ve sign between kx and `omega x`
and `k = sqrta and omega = sqrtb`
But `k = (2pi)/(lamda) = (2pi n)/(n lamda) = (omega)/(v)`
`:. v = (omega)/(k)= sqrt((b)/(a))`
Thus it represents a progressive wave moving in the -x directin, with a speed `sqrt((b)/(a))`. Option (b)
Options (c) and (d) are wrong as it is not a standing wave