3 ms·
While there is certainly a difference between near- and far-field approximations, the short answer is that no, the speakers can be closer than one wavelength to
by sandpaper26 4y ago
While there is certainly a difference between near- and far-field approximations, the short answer is that no, the speakers can be closer than one wavelength together in order to have a steerable far field. In fact, the link you provided has a 1/4 wavelength spaced array as one of its first examples.
You may be confused here because typically it is harder to make lower frequency waves from a single emitter more directional -- but that has more to do with waveguide and aperture geometry.
- eternauta3k 4y agoLooking at the equation for the radiation pattern of the phased array, the angle dependence goes like sin(pi * (N * d/lambda) * sin theta). If N * d (i.e. the size of the array) is much smaller than lambda, there's no interference pattern. To be more precise, for the radiation pattern to have a null, N * d must be larger than the wavelength.
- sandpaper26 4y agoYes, but I think that's why you're confused. The distance between the individual speakers would be d, not N*d. Because your original comment was about this spacing, that's what I addressed in my answer. Obviously a larger effective aperture (either physical or synthetic) would be more effective at beam steering.