Physics · Waves · NEET
At a fixed end the point cannot move at all, so its displacement must always be zero. When an incident crest arrives it pushes the wall up, and by Newton's third law the wall pushes the string back down. This downward reaction sends back an inverted pulse: a crest returns as a trough. Mathematically the reflected wave gains an extra pi in phase: y_r = a sin(kx - wt + pi) = -a sin(kx - wt). The minus sign is the flip.
A free end (like a string tied to a light ring that slides freely on a rod, or the open end of an organ pipe) is free to move. Nothing forces its displacement to zero, so it moves the maximum amount. The incident crest arrives, lifts the free end, and the pulse reflects back the same way up: a crest returns as a crest. So y_r = a sin(kx - wt + 0) = a sin(kx - wt). No inversion, no phase change.
A fixed end is always a NODE. Because the wall flips the wave, the incident and reflected waves always cancel there, giving zero displacement (node). A free end is always an ANTINODE. There the two waves add up, and the displacement is twice the amplitude of each pulse (maximum). Remember: Fixed = Node (no motion), Free = Antinode (max motion).
Phase of pi radians = 180 degrees = half a wavelength shift. In shape terms it means the wave is turned upside down. A phase change of pi turns sin into -sin, so every crest becomes a trough and every trough becomes a crest. 'Phase reversal' and 'inversion' mean the same thing as a pi phase change.
Think of a denser medium (or heavier string) as more 'rigid' - it acts like a fixed end, so the reflected wave suffers a pi phase change (inverts). A rarer medium (lighter string) acts like a free end, so the reflected wave has no phase change. This is the same idea used in wave optics for reflection of light at a denser medium.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
A phase change of pi radians (180 degrees). This inverts the wave, so a crest reflects back as a trough. In equation form the reflected wave is y_r = a sin(kx - wt + pi) = -a sin(kx - wt).
Zero. There is no phase change at a free (open) end. The reflected wave is y_r = a sin(kx - wt), same phase and amplitude as the incident wave (assuming no energy loss).
Because the wall holds that point at zero displacement at all times. The inverted reflected wave always cancels the incident wave exactly at the boundary, so a node forms there.
If there is no energy loss, the amplitude of the reflected wave equals that of the incident wave at both a fixed and a free end. Only the phase differs: pi at a fixed end, zero at a free end.
A closed (stopped) end of an organ pipe behaves like a fixed end - it is a displacement node with a pi phase change. The open end of an organ pipe behaves like a free end - it is a displacement antinode with no phase change.
