Use an expression for the far-field radiation from a plane circular piston to create a more accurate model of a column loudspeaker system - you will need to calculate individual source distances / angles out to a receiver point on an arc in front of the column using simple geometry, and then add the contributions radiated by piston sources driven with in-phase velocity.   Assuming the driver radii a=8cm, plot the polar response of the idealised and practical column sources at a number  of different frequencies.