Maximum directivity factor of nth‐order transducers

It is proved using general group‐theoretic and Hilbert‐space methods that the maximum directivity factor obtainable from an nth‐order directional acoustic transducer is (n+1)2, that this most directional transducer is axially symmetric, and that its polar response to sounds arriving from an angle ϑ off axis is proportional toJn/k=0 (2k+1) Pk(cosϑ). Subject Classification: [43]85.40, [43]85.62.It is proved using general group‐theoretic and Hilbert‐space methods that the maximum directivity factor obtainable from an nth‐order directional acoustic transducer is (n+1)2, that this most directional transducer is axially symmetric, and that its polar response to sounds arriving from an angle ϑ off axis is proportional toJn/k=0 (2k+1) Pk(cosϑ). Subject Classification: [43]85.40, [43]85.62.