When a medium is driven by a spatially extended wave source, it is possible that no waves emanate from the driven region and a standing wave occurs inside the region. This case is a nonpropagating wave source. We report numerical observations and theory in one dimension, where the realistic effects of weak dissipation and weak nonuniformity are included. Each of the effects causes a small amount of propagation to occur so that the source becomes quasi-nonpropagating. The amplitude of the outgoing wave compared to the amplitude of the standing wave is substantially reduced for a uniform source compared to a two-point source of the same length, which suggests that the more evenly a source is spread over a fixed length, the less is the relative propagation.

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Due to dissipation, the response inside the source is only an approximate standing wave. Specifically, nodes no longer strictly exist and the response at any two sites is no longer exactly in phase or antiphase, although these effects are very small for weak dissipation.
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