Practice question

**Quantization due to boundaries** leads to discrete harmonic series. Frequency difference between harmonics is f₁, so f₃ - f₁ = 2f₁ = v/L. Understanding node-antinode pattern explains resonance and overtones in strings. For fixed ends: v_n = (n v/2L) . First harmonic ( n = 1 ): v₁ = (60/2 × 2) = (60/4) = 15 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 15 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.