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

SymbolWhat it stands for
aAmplitude 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.