General idea (with strings): When a wave in a string in transmitted through 2 different media, a part of it is inverted and a part transmitted.
'Rules:' If a wave enters a region where the wave velocity is smaller, the reflected wave is inverted. If it enters a region where the wave velocity is larger, the reflected wave is not inverted. The transmitted wave is never inverted.
Question: What are the reasons for the ‘rules’? Why must it be that the reflected wave is inverted with respect to the original if the incident wave is from a lighter medium i.e.a region where the wave velocity is smaller or vice versa? And why is the transmitted wave never inverted?
My attempts to understand it would be on the basis of light. The wave inversion analogy is also used to explain the behaviour of the phase change of light through 2 different medium. This would imply the refracted wave is never inverted/undergoes a phase change whereas the reflected wave may undergo a phase change depending on the incident wave (it is generally understood as a phenomenon hence w/o a reason). I figure it could be in line with the reason for how light refracts from Huygens principle to electromagnetic wave propagation in the electrons of said medium etc.
However, it doesn’t help me understand the same for mechanical waves.
