Practice question

**Standing wave in fixed string** has nodes at ends, quantizing modes. Fundamental n=1 has λ₁ = 2L, higher harmonics multiples of fundamental f₁. Third harmonic n=3 has three half-wavelengths in length L, f₃ = 3v/(2L), illustrating standing wave condition and boundary enforcement. The boundary condition (node at the closed end, antinode at the open end) requires the wavelength to fit L = (2n - 1) (λ/4) , allowing only odd multiples of the fundamental. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Boundary conditions, illustrating frequency-length-speed interdependence and quantization by boundaries.