Standing Wave Equation (y(x,t) = 2a sin(kx) cos(ωt))
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y(x,t) = 2a sin(kx) cos(ωt)
What each symbol means
| Symbol | What it stands for |
|---|---|
| a | Amplitude of each constituent travelling wave |
| cos(ωt) | Time-dependent factor — all points oscillate in phase |
| 2a sin(kx) | Amplitude at position x — varies with position |
When to use this
Formed by superposition of two identical waves travelling in opposite directions. Nodes at x = nλ/2 (zero displacement always). Antinodes at x = (2n+1)λ/4 (maximum displacement). All particles between two nodes vibrate in phase. Distance between consecutive nodes = λ/2. No energy transport. NCERT Eq. 14.37.