Q.If sound waves are reflected from the surface of a denser medium, there is a phase change of ______. (A) $0$ rad
(B) $\dfrac{\pi}{4}$ rad
(C) $\dfrac{\pi}{2}$ rad
(D) $\pi$ rad

Reflection is what happens when a progressive wave, travelling through one medium, reaches an interface with a second medium: part of the wave's energy returns into the original medium, with its direction of travel reversed. Whether the reflected wave is inverted (undergoes a phase change of $\pi$ radians) or not depends entirely on whether the medium on the FAR side of the boundary is denser or rarer than the medium the wave is currently travelling in.

For a TRANSVERSE wave (e.g. on a string): reflection at a boundary with a DENSER medium (such as a string's end tied to a rigid, immovable support) inverts the wave -- a crest returns as a trough, a $\pi$-radian phase change -- because the fixed point cannot move, so by Newton's third law the string experiences an equal and opposite reaction. Reflection at a boundary with a RARER medium (such as a string's end tied to a freely-sliding, frictionless ring) produces NO phase change -- a crest returns as a crest -- because the free end genuinely moves with the disturbance rather than resisting it. …