We consider traveling transverse waves on two identical uniform taut strings that are elastically coupled through springs that gradually decrease their stiffness over a region of finite length. The wave system can be decomposed into two modes: an in-phase mode ([Formula: see text]) that is transparent to the coupling springs, and an out-of-phase mode ([Formula: see text]) that engages the coupling springs and can resonate at a particular location depending on the excitation frequency. The system exhibits linear mode conversion whereby an incoming ([Formula: see text]) wave is reflected back from the resonance location both as a propagating ([Formula: see text]) wave and an evanescent ([Formula: see text]) wave, while both types emerge as propagating forward through the resonance location. We match a local transition layer expansion to the WKB expansion to obtain estimates of the reflection and transmission coefficients. The reflected waves may be an analog for stimulated emissions from the ear.