$\huge \Delta P = -\beta \frac{\Delta V}{V} $ Where $\beta$ denotes the [[Boltzman Constant]]/ [[Bulk Modulus]] of. the medium, and $V,\Delta V$ representing the [[Volume]] and change in volume. ### Longitudinal Pressure Waves $\huge \begin{align} \Delta P &= -\beta \frac{\Delta V}{V} \\ &= -\beta \partial_{x}^{2}\set{D} \\ &= \beta Ak\cos(kx-\omega t) \end{align}$ $\begin{align} \Delta P &= \Delta P_{m} \cos(kx-\omega t) \\ \Delta P &= \Delta P_{m} \cos(kx \pm \omega t + \phi) \\ \Delta P &= \Delta P_{m} \sin(kx \pm \omega t + \phi) \end{align}$