Quasi-nonpropagating wave sources in one dimension

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.