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Waves transport energy through a medium (or vacuum, for EM waves) without transporting matter. Mechanical waves require a medium and come in two types: transverse (vibration perpendicular to propagation, e.g., string waves) and longitudinal (vibration parallel, e.g., sound in air). The wave equation $y = A\sin(kx - \omega t)$ encodes all information: amplitude $A$, wave number $k = 2\pi/\lambda$, angular frequency $\omega = 2\pi f$, and wave speed $v = \omega/k = f\lambda$.

For JEE, the wave chapter divides into four major areas: progressive wave properties, standing waves in strings and pipes, beats, and the Doppler effect. Standing waves (formed by superposition of counter-propagating identical waves) are central to understanding musical instruments and resonance phenomena. Beats provide a practical method for frequency measurement. The Doppler effect explains the apparent frequency shift when source or observer moves relative to the medium.

The speed of a wave depends on the medium: $\sqrt{T/\mu}$ for strings, $\sqrt{\gamma RT/M}$ for sound in gas, $\sqrt{Y/\rho}$ for longitudinal waves in solids. Understanding these speed formulas and their dependencies (temperature, tension, density) is crucial for solving numerical problems.