Q.Explain the reflection of transverse and longitudinal waves from a denser medium and a rarer medium.

On reflection from a denser medium a wave suffers an abrupt phase reversal ($\pi$); on reflection from a rarer medium, no phase reversal occurs, for both transverse and longitudinal waves.

Reflection from a denser medium (rigid boundary):

When a wave travelling in a rarer medium is reflected at the boundary of a denser medium (treated as a fixed/rigid end), it undergoes a phase reversal of $\pi$ (180°) — i.e. a crest is reflected as a trough (transverse wave), or a compression is reflected as a rarefaction (longitudinal wave). Mathematically, if the incident wave is $y_i = a\sin(\omega t-kx)$, the reflected wave becomes $y_r = -a\sin(\omega t+kx) = a\sin(\omega t+kx+\pi)$. Physically this happens because the denser/rigid boundary cannot itself move (or moves much less), so it exerts an equal and opposite reaction, inverting the wave.

Reflection from a rarer medium (free boundary):

When a wave is reflected at the boundary of a rarer medium (treated as a free end), there is no phase change — a crest reflects as a crest, a compression reflects as a compression. Here $y_r = a\sin(\omega t+kx)$ (no extra $\pi$), since the free boundary can move without opposition, and the reflected disturbance simply retraces the same displacement sense.

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