reciprocity theorem

reciprocity theorem [‚res·ə′präs·əd·ē ‚thir·əm]

Also known as principle of reciprocity.

(acoustics)

The theorem that, in an acoustic system consisting of a fluid medium with boundary surfaces and subject to no impressed body forces, ifp₁andp₂are the pressure fields produced respectively by the components of the fluid velocitiesV₁andV₂normal to the boundary surfaces, then the integral over the boundary surfaces ofp₁V₂-p₂V₁vanishes.

(electricity)

The electric potentialsV₁andV₂produced at some arbitrary point, due to charge distributions having total charges ofq₁andq₂respectively, are such thatq₁V₂=q₂V₁.

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.

(electromagnetism)

Given two loop antennas,aandb, thenI_ab/V_a=I_ba/V_b, whereI_abdenotes the current received inbwhenais used as transmitter, andV_adenotes the voltage applied ina;I_baandV_bare the corresponding quantities whenbis the transmitter,athe receiver; it is assumed that the frequency and impedances remain unchanged.

(engineering acoustics)

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.

(physics)

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.