Physics · Waves · NEET
In a travelling wave the term looks like sin(kx - wt), where x and t are mixed together, so a fixed crest moves along as time passes. When you add two opposite waves you get y = 2a sin(kx) cos(wt). Now x sits only inside sin(kx) and t sits only inside cos(wt). The shape sin(kx) is fixed in space; cos(wt) only changes the size up and down. So the pattern stays put and just breathes in and out - that is why we call it stationary.
Usually from reflection. You send one wave down a string or air column; it hits a fixed end (wall, closed end) or free end and bounces back. The reflected wave has the same amplitude and frequency but travels the opposite way. The original wave and its reflection overlap and form the standing wave. This is why standing waves appear on guitar strings and inside organ pipes - the wave keeps reflecting between the two ends.
It is a real, observable pattern, but it is produced by interference (superposition). At some points the two waves always cancel (nodes, zero movement) and at others they always add (antinodes, biggest movement). Nothing is fake - you can see the fixed still points and the large-swing points on a vibrating string. It is a special, steady interference pattern, not a new kind of wave.
No net energy is carried from one end to the other. In a travelling wave energy flows in the direction of motion. In a standing wave the two opposite waves carry equal energy in opposite directions, so the flows cancel. Energy just sloshes back and forth between kinetic (at antinodes, moving fast) and potential (near nodes, stretched), trapped in each loop.
Yes, for a clean standing wave. Same frequency keeps the pattern steady in time; same amplitude makes the nodes fully still (zero). If amplitudes differ, the nodes never reach perfect zero and the pattern partly drifts, so it is not a pure standing wave. For NEET, assume equal amplitude and equal frequency travelling in opposite directions.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
y = 2a sin(kx) cos(wt). Here 2a sin(kx) is the amplitude that depends on position x, and cos(wt) is the time part. It comes from adding y1 = a sin(kx - wt) and y2 = a sin(kx + wt).
(1) The two waves must have the same amplitude and same frequency. (2) They must travel in exactly opposite directions. In practice the second wave is usually a reflection of the first.
A travelling wave (y = a sin(kx - wt)) moves and carries energy. A standing wave (y = 2a sin(kx) cos(wt)) does not move; it has fixed nodes and antinodes and carries no net energy across.
It is the base idea behind organ pipes, sonometer strings, and resonance columns - all frequent NEET topics. If you understand y = 2a sin(kx) cos(wt) and where nodes sit, harmonics and frequency problems become easy.
