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 ($$+$$+) that is transparent to the coupling springs, and an out-of-phase mode ($$-$$-) 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 ($$+$$+) wave is reflected back from the resonance location both as a propagating ($$+$$+) wave and an evanescent ($$-$$-) 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.

中文翻译：

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耦合弦的受激声发射

我们考虑在两个相同的均匀拉紧弦上传播横波，这些弦通过弹簧弹性耦合，弹簧在有限长度的区域内逐渐降低其刚度。波系统可以分解为两种模式：对耦合弹簧透明的同相模式 ($$+$$+) 和使耦合弹簧接合的异相模式 ($$-$$-)耦合弹簧并可根据激励频率在特定位置共振。该系统表现出线性模式转换，其中传入 ($$+$$+) 波从共振位置反射回，既作为传播 ($$+$$+) 波又作为渐逝 ($$-$$-) 波，而这两种类型都是通过共振位置向前传播。我们将局部过渡层扩展与 WKB 扩展相匹配，以获得反射和透射系数的估计值。反射波可以模拟来自耳朵的受激发射。