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JeansInstability

-              v1
+              v2
 [[latex($\frac{\partial^2\rho_1}{\partial t^2} - C_s^2 \triangledown^2 \rho_1 - 4\pi G \rho_0 \rho_1 = 0$)]]
+where
+[[latex($\rho_1 \equiv density ~perturbation$)]]
+[[latex($C_s \equiv sound ~speed$)]]
+where [[latex($C_s$)]] is the sound speed.
 This is a wave equation, so we propose a solution of the form:
 …
 [[latex($ \rho_1(\vec{x},t) = C e^{i(\vec{k} \cdot \vec{x} - \omega t)}$)]]
 Plugging this into the wave equation above gives the following dispersion relation:
+where the wave number k is given by [[latex($k = 2 \pi /\lambda$)]], with [[latex($\lambda$)]] specifying the perturbation oscillation wave length, and [[latex($\omega$)]] is the angular frequency of oscillation given by [[latex($\omega = 2 \pi f$)]]. Plugging this into the wave equation above gives the following dispersion relation:
 [[latex($\omega ^2 = C_s^2 k^2 - 4 \pi G \rho_0$)]]