# For two strings tied together: Why does a sinusoidal incident wave give rise to sinusoidal reflected and transmitted waves? [duplicate]

I am reading Griffiths' Intro to Electrodynamics (Section 9.1.3 Boundary Conditions: Reflection and Transmission) where he analyzes the case of an incident wave sent down a string that is tied to another string. The first string has uniform mass per unit length $$\mu_1$$ and the second has uniform mass per unit length $$\mu_2$$.

He says the incident wave is a sinusoidal oscillation that extends (in principle) all the way back to $$z=-\infty$$ (defining $$z$$ the axis along the length of the string) and that the same goes for the reflected wave and transmitted wave (except $$z=+\infty$$ for the transmitted wave).

I'm not entirely sure what's confusing me, but I'll start with this question:

What guarantees that the transmitted and reflected waves are sinusoidal?