Spherical vs. Cylindrical Wavefront Divergence & Amplifier Crest Factor

A single point-source loudspeaker radiates sound omnidirectionally (or into a constant spherical solid angle), spreading its acoustic power over a surface area proportional to $4\pi r^2$. Consequently, sound intensity drops with the square of distance ($I \propto 1/d^2$), translating to $-6.02\text{ dB}$ of SPL loss for every doubling of distance.

By contrast, a vertical line array of length $L$ creates a coherent cylindrical wavefront within its near-field Fresnel region ($d \le d_{\text{border}}$). Because a cylinder’s surface area expands linearly with radius ($A = 2\pi r L$), acoustic energy decays at only $-3.01\text{ dB}$ per distance doubling until reaching the transition distance $d_{\text{border}}$, beyond which spherical $-6\text{ dB}$ divergence resumes.