Why does a PHASE change take place during reflection of waves from a rigid support?

Because the wave, vibration of the medium particles, longitudinal or transverse, can't be continued with the particles of a rigid support. A rigid support is one which is made of particles which can't be deformed. Hence, when particles of the medium are vibrating and carrying the wave forward and suddenly meets a rigid support, the wave energy can't set vibrations in the rigid support, so instead, the vibrations are reversed in the medium particles immediately near the rigid support in the opposite manner, like from compression to rarefactions, or crest to trough.

This is what is meant by a phase change. Just as if a ball hits a wall it's direction of velocity is completely reversed, the phase of a wave is changed by π.

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TopperLearning.