Practice question

**Resonance in pipes** occurs when length accommodates standing wave pattern. Closed pipe L = (2n-1)λ/4, so f₁ = v/(4L). Given f₁ and v, length follows L = v/(4f₁), enabling length calculation from measured resonance frequency and sound speed 330-340 m/s. For open pipe: v_n = (n v/2L) . Third harmonic ( n = 3 ): v₃ = (3 × 340/2 × 0.51) = (1020/1.02) = 1000 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1000 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.