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. For fixed ends: v_n = (n v/2L) . Second harmonic ( n = 2 ): 80 = (2 × v/2 × 1) . 80 = (v/1) ⇒ v = 80 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 80 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.