Infrasound observations are increasingly used to constrain properties of volcanic eruptions. In order to better interpret infrasound observations, however, there is a need to better understand the relationship between eruption properties and sound generation. Here we perform two‐dimensional computational aeroacoustic simulations where we solve the compressible Navier‐Stokes equations for pure‐air with a large‐eddy simulation approximation. We simulate idealized impulsive volcanic eruptions where the exit velocity is specified and the eruption is pressure‐balanced with the atmosphere. Our nonlinear simulation results are compared with the commonly used analytical linear acoustics model of a compact monopole source radiating acoustic waves isotropically in a half space. The monopole source model matches the simulations for low exit velocities ( m/s or where is the Mach number); however, the two solutions diverge as the exit velocity increases with the simulations developing lower peak amplitude, more rapid onset, and anisotropic radiation with stronger infrasound signals recorded above the vent than on Earth's surface. Our simulations show that interpreting ground‐based infrasound observations with the monopole source model can result in an underestimation of the erupted volume for eruptions with sonic or supersonic exit velocities. We examine nonlinear effects and show that nonlinear effects during propagation are relatively minor for the parameters considered. Instead, the dominant nonlinear effect is advection by the complex flow structure that develops above the vent. This work demonstrates the need to consider anisotropic radiation patterns and jet dynamics when interpreting infrasound observations, particularly for eruptions with sonic or supersonic exit velocities.