Multiple choice

The equation $k_x\frac{\partial^2h}{\partial x^2} + k_z \frac{\partial ^2h}{\partial z^2} = 0$can be transformed to$\frac{\partial^2h}{\partial x_1^2} + \frac{\partial ^2h}{\partial z^2} = 0$by substituting

  1. $x_1 = x \frac{k_z}{k_x}$
  2. $x_1 = x \frac{k_x}{k_z}$
  3. $x_1 = x \sqrt{\frac{k_x}{k_z}}$
  4. $x_1 = x \sqrt{\frac{k_z}{k_x}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To transform the equation kx(d^2h/dx^2) + kz(d^2h/dz^2) = 0 into the Laplace equation, we need to scale the x-coordinate. Substituting x1 = x * sqrt(kz/kx) results in the desired form.