Sound, Interference, Diffraction & Doppler
Wave Equation & Harmonics: Traveling waves satisfy $\frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2}$ with harmonic profile $y(x,t) = A\sin(kx - \omega t + \phi)$, where wave number $k = \frac{2\pi}{\lambda}$, angular frequency $\omega = 2\pi f$, and speed $v = \lambda f$.
Superposition & Standing Waves: Counter-propagating waves form standing waves $y(x,t) = [2A\sin(kx)]\cos(\omega t)$ featuring stationary nodes ($y = 0$) and antinodes ($y = 2A$).
Doppler Frequency Shift: For relative motion between source and observer in a medium with wave speed $v$: $f' = f \left(\frac{v \pm v_o}{v \mp v_s}\right)$.
Operating Instructions: Use the sidebar tab switcher to explore Sound wave harmonics, 2D Wave interference patterns, Standing wave nodes, and Doppler pitch shifts.