Practice question

**Wave equation** y(x,t) = A sin(kx - ωt + φ) describes displacement of progressive harmonic wave, where k = 2π/λ wave number (rad/m), ω = 2πf angular frequency (rad/s), v = ω/k wave speed (m/s). Sign of ωt indicates direction, amplitude A is maximum displacement. In solids, longitudinal waves (P-waves) travel faster than transverse waves (S-waves) because the bulk modulus plus shear modulus exceeds the shear modulus alone, increasing speed. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Longitudinal, illustrating frequency-length-speed interdependence and quantization by boundaries.