Abstract
Making use of the transfer matrices and electroacoustic analogies, a standing wave analysis of the active noise control system in a duct is presented incorporating the characteristics of the primary source, as well as the auxiliary source. Analytical expressions have thus been derived for the ratio of the two source pressures and certain other ratios or relations of interest for complete cancellation of noise downstream of the auxiliary source. These expressions are then compared with those obtained from transfer functions of the various blocks constituting the block diagram of the entire system. In the process, equivalence has been established between the different entities involved in the two approaches, one of which is used in acoustics and the other in system theory. In particular, it has been shown that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against the characteristic impedance and the other by reflecting the rearward wave (incident on the source) off the source impedance. This principle is seminal in linking the two approaches.
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