Calculation of sound pressure level created by arrayed sound sources

I am trying to get a large sound pressure level by arranging individual horns, but I am curious how to design the arrangement structure to obtain a synthetic sound field with sharp directivity in the axial direction given the synthetic sound pressure level and the sound pressure level of the individual horns.

$$Y(\psi) = \frac{1}{N} \frac{\sin \left( N \frac{\psi}{2}\right)}{\sin \left( \frac{\psi}{2}\right)}$$
with $$N$$ the number of elements in the array. Replacing $$\psi$$ with $$\psi = \frac{2 \pi}{\lambda} d \cos (\theta)$$ where $$k$$ is the wavenumber given by $$k = \frac{\omega}{c} = \frac{2 \pi}{\lambda}$$, with $$\lambda$$ being the wavelength, $$c$$ the speed of sound and $$d$$ the distance between the elements, you can get the response of the array for various angles of interest $$\theta$$ for any frequency of interest corresponding to a wavelength $$\lambda$$.