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. v_n = (n v/2L) . First harmonic ( n = 1 ): v₁ = (96/2 × 2.4) = (96/4.8) = 20 Hz . Third harmonic ( n = 3 ): v₃ = (3 × 96/2 × 2.4) = (288/4.8) = 60 Hz . Difference: v₃ - v₁ = 60 - 20 = 40 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 40