# Finding the distance between two osclilating particles in a wave

Assume a wave function $\psi = \psi(x,t)$ where $x$ is position from the starting point $(0,0)$ and $t$ is time. Two oscillating points A and B are located at $x_1$ and $x_2$ respectively with $x_2 \geq x_1$ and $x_1 > vt_1$ where $t_1$ is a moment in time. If I was to find their distance via using calculus could I do this? :

\begin{align}s(x_2,x_1) &= \int^{x_2}_{x_1} ds \\ &= \int^{x_2}_{x_1} \sqrt{(dx)^2 + (d \psi)^2} \\ &= \int^{x_2}_{x_1} \sqrt{(dx)^2 + \bigg(\frac{\partial \psi}{\partial x}dx \bigg)^2} \\ &=\int^{x_2}_{x_1} \sqrt{1 + \bigg(\frac{\partial \psi}{\partial x}\bigg)^2} dx\end{align}

Instead of finding $x = x_2 - x_1$, $y = \psi(x_2,t_1) - \psi(x_1,t_1)$ and then $s(x_2,x_1) = \sqrt{x^2 + y^2}$