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 closed pipe: v_n = (n + (1/2)) (v/2L) , n = 4 for fifth harmonic. v₄ = (4 + (1/2)) (360/2 × 0.45) = 4.5 × (360/0.9) = 4.5 × 400 = 1800 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1800 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.