A loudspeaker is provided for receiving an incoming electrical signal and transmitting an acoustical signal that is directional and has a substantially constant beamwidth over a wide frequency range. The loudspeaker may include a curved mounting plate that has curvature over a range of angles. The loudspeaker may include an array of speaker drivers coupled to the mounting plate. Each speaker driver may be driven by an electrical signal having a respective amplitude that is a function of the speaker driver's respective location on the mounting plate. The function may be a Legendre function. Alternatively, the loudspeaker may include a flat mounting plate. In this case, the respective electrical signal driving each speaker may have a phase delay that virtually positions the speaker onto a curved surface.