Waves & Sound
Wave propagation, interference, Doppler effect, and sound visualization
- NewSchool
Acoustic Levitation (Schematic)
Standing wave cos(kx)cos(ωt); pressure nodes marked; bead cartoon near a node.
- NewSchool
Acoustic Phased Array (Line)
N sources, spacing d/λ and phase ramp: steer audio/sonar-like beams (array factor sketch).
- NewSchool
Chladni Figures
Plate mode sin(mπx)sin(nπy); nodal contrast + grains drift to nodes (model).
- NewSchool
Cymatics: Circular Membrane
Drum eigenmodes J_m(k_{mn}r) cos(mθ); angular m, radial n, shimmer.
- NewSchool
Echo & Echosounder
Round-trip time t = 2d/v; pulse to a wall and back with adjustable sound speed.
- NewSchool
Wave Speed: String vs Rod
v = √(T/μ) for a string vs v ≈ √(E/ρ) for longitudinal bar waves.
- NewSchool
LC Oscillator (Undamped)
Ideal series LC: q(t), I(t), ω₀ = 1/√(LC); U_C + U_L constant; vs RLC AC.
- NewSchool
Larsen Effect (Feedback Loop)
Mic + speaker + delay: loop gain and saturation in a toy discrete feedback model.
- NewUniversity / research
Duffing Oscillator
m x¨+cx˙+kx+k₃x³=F cos ωt; soft/hard spring; A(ω) scan vs IC.
- NewSchool
Wave Packet & Dispersion
Superpose cos(kx−ωt); ω=ck+αk²; spreading vs Wave on String PDE.
- NewSchool
Mach Cone (Schematic)
M = v/c > 1: Huygens pulses + cone sin μ = 1/M; not CFD shock.
- NewSchool
Monochord / Sonometer
f₁ = (1/2L)√(T/μ), harmonics, note label, Pluck; vs Standing Waves shapes.
- NewSchool
Huygens Principle (Slit)
Secondary sources on slit; superposition & diffraction sketch; not full optics.
- NewUniversity / research
Forced Nonlinear Pendulum
θ¨+γθ˙+(g/L)sinθ=A cosωt; phase plot; vs Double Pendulum 2-DOF.
- NewSchool
Seismic P and S (Schematic)
Longitudinal vs transverse particle motion; v_P, v_S sliders — not layered Earth.
- NewSchool
Water Wave Dispersion ω(k)
Shallow k√(gh), deep √(gk), full tanh(kh) — three curves.
- NewUniversity / research
Tsunami & Shallow Water (1D)
Linear η,u on H(x): c = √(gH) drops over shelf; Gaussian uplift impulse.
- NewUniversity / research
Storm Surge Bathtub + Wind Setup
Inverse barometer pressure setup plus wind stress τL/(ρgH) over a shelf; coastal water level and tide timing toy.
- NewSchool
Tide Constituents & Beats
M2/S2/K1/O1 harmonic superposition, spring-neap beat cycle, diurnal inequality, and an amphidromic phase cartoon.
- NewSchool
Kelvin Ship Wake (Cusp Angle)
Deep-water wake V: arms at arcsin(1/3) ≈ 19.47° each side of the track (idealized).
- NewUniversity / research
KdV Solitons (Exact)
u_t + 6uu_x + u_xxx = 0; Hirota two-soliton collision or one sech² pulse.
- FeaturedSchool
Wave on a String
Shake one end, adjust frequency and amplitude. Standing waves and reflections.
- School
Transverse vs Longitudinal
Side-by-side comparison of wave types with particle motion.
- FeaturedSchool
Wave Interference
Two sources creating constructive and destructive patterns. 2D ripple tank.
- School
Standing Waves
Find harmonics on a string. Nodes and antinodes highlighted.
- NewSchool
Doppler Effect
Moving source with pitch change via Web Audio. Wavefront compression visible.
- NewUniversity / research
Light Doppler & Redshift
EM vacuum Doppler: f/f₀ and z vs v/c; linear Δλ/λ ≈ v/c vs exact √(1+β)/√(1−β). Ties to spectral lines.
- NewSchool
Room Reverberation (2D rays)
Specular rays in a shoebox plan; impulse response; RT60 vs Sabine. Absorption per bounce.
- NewSchool
Active Noise Cancellation (1D)
Two tones same f: amplitudes and phase; RMS sum vs ideal π phase. Destructive interference demo.
- NewUniversity / research
Beam Modal Analysis (Euler–Bernoulli)
First three bending modes: λ from BC; f ∝ (λ/L)²√(EI/μ). Pinned, cantilever, clamped.
- NewSchool
Group & Phase Velocity
Two-wave beat: ω(k)=ck+αk²; v_g=Δω/Δk vs v_p=ω̄/k̄; envelope vs carrier.
- NewSchool
Organ Pipe (harmonic series)
Open–open vs stopped: f_n formulas; pressure shape; table of modes; Web Audio.
- School
Sound Wave Visualizer
Real-time waveform and frequency spectrum from microphone.
- School
Beat Frequency
Two slightly different frequencies creating audible beats.
- NewSchool
Resonance Tube
Open vs closed pipe harmonics. Hear fₙ and see standing pressure wave.
- NewSchool
Hearing & Loudness (sketch)
Qualitative threshold vs frequency; compare to equal-loudness ideas.
- NewUniversity / research
2D Wave Equation (Membrane)
Explicit FDM on a clamped rectangle: Gaussian pulse, circular fronts, edge reflections.