reciprocity theorem(redirected from Reciprocity (mathematics))
Also found in: Wikipedia.
reciprocity theorem[‚res·ə′präs·əd·ē ‚thir·əm]
Also known as principle of reciprocity.
The theorem that, in an acoustic system consisting of a fluid medium with boundary surfaces and subject to no impressed body forces, if p1 and p2 are the pressure fields produced respectively by the components of the fluid velocities V1 and V2 normal to the boundary surfaces, then the integral over the boundary surfaces of p1 V2-p2 V1 vanishes.
The electric potentials V1 and V2 produced at some arbitrary point, due to charge distributions having total charges of q1 and q2 respectively, are such that q1 V2= q2 V1.
In an electric network consisting of linear passive impedances, the ratio of the electromotive force introduced in any branch to the current in any other branch is equal in magnitude and phase to the ratio that results if the positions of electromotive force and current are exchanged.
Given two loop antennas, a and b, then Iab / Va = Iba / Vb , where Iab denotes the current received in b when a is used as transmitter, and Va denotes the voltage applied in a ; Iba and Vb are the corresponding quantities when b is the transmitter, a the receiver; it is assumed that the frequency and impedances remain unchanged.
The sensitivity of a reversible electroacoustic transducer when used as a microphone divided by the sensitivity when used as a source of sound is independent of the type and construction of the transducer.
In general, any theorem that expresses various reciprocal relations for the behavior of some physical systems, in which input and output can be interchanged without altering the response of the system to a given excitation.