TITLE: Parabolic speaker dish diameter
QUESTION [0 upvotes]: I am trying to design a parabolic speaker to allow an audio signal to be emitted in only a single direction. For a single acoustic tone with wavelength $w$, what should the diameter of the reflector dish be? Wikipedia states that the diameter should be at least twice the wavelength, but does not explain why.

REPLY [0 votes]: Three main reasons:  

reduce diffraction/interference related effects (occur when $\lambda$~D)  
increase directionality (beamwidth $\propto \frac\lambda D$)  
increase gain ($\propto \left(\frac D \lambda \right)^2$)

where $\lambda$ is sound's wavelength and D the dish's aperture.  
As to why the minimum limit of $D/\lambda$ is suggested to be $2$: I think its a rule of thumb heuristic motivated by practical engineering. In real world applications, the ratio would in fact be higher and its minimum would be decided by the min-max of supported bandwidth.
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