When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the transmitted wave is in phase with respect to the incident wave. Both the reflected and the transmitted waves have amplitudes less than the amplitude of the incident wave. If the tension in both the strings is the same, the wave speed is lower in the string with higher linear mass density.
In contrast, consider the propagation of waves from a string of high linear mass density to low linear mass density string. In such a case, the reflected wave is in phase with respect to the incident wave, as is the transmitted wave. Both the reflected and the transmitted waves have amplitudes less than the amplitude of the incident wave.
This text is adapted from Openstax, University Physics Volume 1, Section 16.5: Interference of Waves.
