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I am consistently obsessed with transmitting as much audible sound as possible. A lot of progress has been made with your help.
What I would like to ask is to increase the frequency moderately in order to transmit the audible sound further, and to increase the near field distance by arranging the loudspeaker in a rectangular shape. Given a frequency, loudspeaker dimensions and arrangement, how do we calculate the boundary between the near field and the circle field?
The standard rule of thumb is that the transition between near field and far field is less than or equal to about one wavelength at the lowest frequency you wish to radiate. This means for maximum radiation, the dimension l of a square array of loudspeakers must be made about equal to the cutoff frequency f of the system. For f = 1000Hz, l is about one foot. For 100Hz, l becomes 10 feet and 50Hz yields l = 20 feet, etc.
You can see that to bathe the listener in near-field sound requires an enormous speaker array. The band Grateful Dead actually assembled and toured with just such a system in the early 1970's, for just that reason. The band members stood in front of a speaker array 20 feet tall which stretched across the entire stage.
It was loud and impressive, but ultimately impractical.
Borrowing from the RF world, a rule of thumb for defining the far field distance, $d_{ff}$, is: $$d_{ff} \geq \frac{2D^2}{\lambda}$$ where $D$ is the maximum linear distance of the radiating array and $\lambda$ is the wavelength of the radiated signal.
