Potential (V) at a point in space is given by `v=x^(2)+y^(2)+z^(2)`. Gravitational field at a point (x,y,z) is

Options

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

Answer

B

Explanation

`y(x,t)=e^(-(ax^(2)+bt^(2)+2sqrt(ab)xt))=e^(-(sqrt(ax)+sqrt(bt))^(2)`
Comparing equation (i) with standard equation `y(x,t) = f(ax + bt)`
As there is positive sign between x and t terms, hence wave travel in `-x` direction.
Wave speed = `("Coefficient of t")/("Coefficient of x")= sqrt((b)/(a)).`