Practice question

**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. In a standing wave, interference of two opposite-traveling waves creates nodes (zero amplitude) and antinodes (maximum amplitude), causing spatial variation due to phase alignment. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Due to interference, illustrating frequency-length-speed interdependence and quantization by boundaries.