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. Form: y = A sin (kx) cos (ω t) , k = (π/3) rad/m . Wavelength: λ = (2π/k) = (2π/(π/3)) = 6 m . Distance between node and antinode: (λ/4) = (6/4) = 1.5 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1.5 m, illustrating frequency-length-speed interdependence and quantization by boundaries.