Chapter 15: Mechanical Waves

The fundamental wave types include transverse waves where particle motion occurs perpendicular to wave direction, longitudinal waves where particles oscillate parallel to propagation direction, and surface waves that combine both motions. Mathematical wave functions describe periodic wave behavior using parameters such as amplitude, wavelength, frequency, and wave speed, with sinusoidal waves following the relationship v = λf and satisfying the general wave equation. Wave speed depends critically on medium properties, exemplified by waves on strings where velocity equals the square root of tension divided by linear mass density. Energy transport represents a crucial wave property, with average power proportional to the square of both frequency and amplitude, while three-dimensional wave propagation follows inverse-square intensity relationships. The superposition principle governs wave interactions, producing constructive interference when waves reinforce and destructive interference when waves cancel, with boundary conditions determining reflection characteristics at fixed or free endpoints. Standing wave patterns emerge from interference between incident and reflected waves, creating stationary nodes and antinodes with specific spatial distributions. For strings fixed at both ends, resonant frequencies form harmonic series where the fundamental frequency and overtones depend on string length, tension, and mass density, providing the physical foundation for musical instrument design and acoustic phenomena.