How waves reflect at the ends of a medium, or at the interface between two media, is critical to understanding things like musical instruments.

When a wave encounters a fixed end, for instance, it comes back upside down.

When a wave encounters a free end, it comes back the same way it went out.

When a wave traveling in a medium encounters a boundary with a lower-velocity medium (i.e., the wave speed is lower in the other medium) part of the wave is reflected and part is transmitted. For the reflected part, the boundary acts like a fixed end and the reflected wave is inverted.

When the wave encounters a higher-velocity medium there is also some reflection and some transmission of the wave. This time the boundary acts like a free end and the reflected wave is upright.