A General Proof of the Reciprocity Theorem for Electroacoustic Transducers
| Autor: | Leslie L. Foldy, Henry Primakoff |
|---|---|
| Rok vydání: | 1945 |
| Předmět: |
Acoustics and Ultrasonics
Basis (linear algebra) Microphone Acoustics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Wave equation Surface (topology) Integral equation Symmetry (physics) Distribution (mathematics) Transducer Arts and Humanities (miscellaneous) Computer Science::Sound Computer Science::Formal Languages and Automata Theory Mathematics |
| Zdroj: | The Journal of the Acoustical Society of America. 17:102-102 |
| ISSN: | 0001-4966 |
| DOI: | 10.1121/1.1902402 |
| Popis: | On the basis of a general theory of the operation of passive linear transducers developed by the authors, a proof of the reciprocity theorem for electroacoustic transducers is presented together with the conditions necessary for its validity. The reciprocity theorem states that the ratio of the microphone response to the speaker response for an electroacoustic transducer is a quantity which, under certain general conditions, is independent of the specific nature and construction of the transducer. This quantity is 2d/ρf where ρ is the density of the medium, f is the frequency, and d is the distance from the center of the transducer to the point where the pressure is measured in obtaining the speaker response. The center of the transducer is defined as the point where the incident pressure is measured, in the absence of the transducer, when obtaining the microphone response. The general theory referred to above assumes a pair of the most general equations (in this case, integral equations), relating the pressure and normal velocity at each point on the surface of the transducer and the voltage and current at its terminals. These, together with the appropriate solutions of the wave equation derived by the use of Green's functions and relating the pressure at any point in the medium to the normal velocity distribution on the transducer surface, completely characterize the behavior of the transducer and allow explicit calculation of the responses. The validity of the reciprocity theorem then requires certain symmetry conditions on the parameters entering into the equations. The relation between these symmetry conditions and the physical characteristics of the transducer allow the limits of validity of the reciprocity theorem to be delineated. |
| Databáze: | OpenAIRE |
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