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. In a standing wave, antinodes are points of maximum displacement, occurring every half wavelength. Thus, the distance between consecutive antinodes is λ/2 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Half the wavelength, illustrating frequency-length-speed interdependence and quantization by boundaries.