[![enter image description here](https://i.stack.imgur.com/EmvGm.jpg)](https://i.stack.imgur.com/EmvGm.jpg)

In a MIT OCW video lecture, a professor discusses a wave on a string having some density moving towards another string. Both of which are joined but have different densities.

He goes on to analyse it, but assumes a reflected wave and a transmitted wave to be present as the wave strikes the boundary. He further assumes that the frequency of the reflected and transmitted wave are the same as the incident one. He doesn't give an explanation, but how can one assume these?

What if we get back some arbitrary wave with different frequency than the incident one bouncing back and nothing as a transmitted wave?

What justifies these assumptions which the professor made?

I'd be glad if someone pointed out.