Please correct me if I'm misstaken but,
The directivity factor, or the "narrowness" of the beam is dependent of the wavelength for a given geometry.
Once upon a time, we had a carrierfreq. and a baseband-signal for radio where the bandwidth of the baseband-signal << carrier-frequency and we used FM/AM modulation, thus the beam had about the same directivity over the used frequency band for the radio transmission and everything worked fine.
For microphones you solved the problem with shoot-gun microphones like this to create acoustic delay-lines.
But the penalty of such construction in general is the frequency response and the frequrncy dependent directivity factor.
For Audio we would like to have a microphone that covers 20Hz-20kHz, at least for human speech we need to cover the voice-formants 300-3800 Hz + the consonants, thus 300 Hz- 8 kHz.
If we now try to create a "zoom"-microphone we get the problem with the directivity since the frequency covers over one decade.
A solution to achieve a beam with a frequency-independent narrowness, and a final result that has a flat frequency response, is to apply a filter-function to each signal prior addition - and in the end make a compensation with a filter if necessary.
Simpe array-antennes for EM. could be used a long time ago, since it was simple to construct a short-time delay-paths, and the bandwidth of the baseband was very narrow.
