The tips of large horizontal-axis wind turbines can easily reach high speeds, thus raising the concern that compressibility effects may influence turbine wakes and ultimately power production. All past studies have assumed that these effects are negligible. Compressibility effects are assessed here in terms of blade aerodynamic properties and variable density separately. Using the Blade Element Momentum (BEM) method, we find that under normal operating conditions (i.e., wind speed < similar to 15 m s(-1) and tip speed ratio TSR < similar to 12) aerodynamic corrections to the lift and drag coefficients of the blades have a minimal impact, thus the incompressible coefficients are adequate. To assess the variable-density effects, numerical simulations of a single turbine and two aligned turbines, modeled via the actuator line model with the default aerodynamic coefficients, are conducted using both the traditional incompressible and a compressible framework. The flow field around the single turbine and its power performance are affected by compressibility and both show a strong dependency on TSR. Wind speed and turbulent kinetic energy (TKE) differences between compressible and incompressible results origin from the rotor tip region but then impact the entire wind turbine wake. Power production is lower by 8% under normal operating conditions (TSR similar to 8) and 20% lower for TSR similar to 12 due to compressibility effects. When a second turbine is added, the front turbine experiences similar effects as the single-turbine case, but TKE differences are enhanced while wind speed differences are reduced after the second turbine in the overlapping wakes. These findings suggest that compressibility effects play a more important role than previously thought on power production and, due to the acceptable additional computational cost of the compressible simulations, should be taken into account in future wind farm studies.