Recently, Squire & Hopkins (2017) showed any coupled dust-gas mixture is subject to a class of linear 'resonant drag instabilities' (RDI). These can drive large dust-to-gas ratio fluctuations even at arbitrarily small dust-to-gas mass ratios. Here, we identify and study both resonant and new non-resonant instabilities, in the simple case where the gas satisfies neutral hydrodynamics and supports acoustic waves ($ω^{2}=c_{s}^{2}\,k^{2}$). The gas and dust are coupled via an arbitrary drag law and subject to external accelerations (e.g. gravity, radiation pressure). If there is any dust drift velocity, the system is unstable. The instabilities exist for {\em all} dust-to-gas ratios $μ$ and their growth rates depend only weakly on $μ$ around resonance, as $\simμ^{1/3}$ or $\sim μ^{1/2}$ (depending on wavenumber). The behavior changes depending on whether the drift velocity is larger or smaller than the sound speed $c_{s}$. In the supersonic regime a 'resonant' instability appears with growth rate increasing without limit with wavenumber, even for vanishingly small $μ$ and values of the coupling strength ('stopping time'). In the subsonic regime non-resonant instabilities always exist, but their growth rates no longer increase indefinitely towards small wavelengths. The dimensional scalings and qualitative behavior of the instability do not depend sensitively on the drag law or equation-of-state of the gas. The instabilities directly drive exponentially growing dust-to-gas-ratio fluctuations, which can be large even when the modes are otherwise weak. We discuss physical implications for cool-star winds, AGN-driven winds and torii, and starburst winds: the instabilities alter the character of these outflows and could drive clumping and/or turbulence in the dust and gas.

18 pages (+appendices), 5 figures. Updated with minor corrections and extended discussion of behavior in stratified systems, and to match published (MNRAS) version