物理
通过交互模拟探索物理原理
103 个工具
Electric Field Lines - Point Charge Visualization - 点电荷电场线
Interactive electric field lines visualization demonstrating Coulomb's law, superposition principle, and equipotential surfaces. Features electric field formula: E = kQ/r² · r̂. Superposition principle: E_total = ΣE_i. Electric potential: φ = kQ/r. Field line equation: dr/E = dx/E_x = dy/E_y. Real-time visualization includes: (1) Electric field lines (red) emanating from positive charges and terminating on negative charges with adjustable density; (2) Equipotential lines (dashed) showing constant potential surfaces perpendicular to field lines; (3) Optional field vectors showing direction and magnitude with arrow spacing control; (4) Interactive charges with click-to-add, drag-to-move, and double-click-to-remove functionality. Adjustable parameters: charge magnitude (-10 to +10 μC), line density (8-32 lines per charge), field intensity scale (0.5-2.0x), equipotential levels (4-16), and arrow spacing (20-80 px). Preset configurations: electric dipole (±5 μC separated), quadrupole (four charges in square arrangement), two positive charges, two negative charges, and clear all. Educational content covers Coulomb's law and electric field calculation, properties of electric field lines (never cross, tangent shows field direction, density ∝ field strength, start on positive and end on negative, number of lines ∝ charge magnitude), equipotential lines (constant potential, perpendicular to field lines, concentric circles for point charge), electric dipole characteristics (p = Qd), and practical applications: capacitor design, molecular structure and chemical bonding, particle accelerators, electrostatic precipitation, medical imaging (EEG/EKG), lightning protection, and plasma physics research. Color coding: red for positive charges, blue for negative charges, with glow effects and animated field direction arrows. Multi-language support (zh, en, es, fr, de, ru, pt).
Polarized Light - 偏振光
Interactive polarized light simulation demonstrating Malus's law, polarizer action, and wave polarization. Features Malus's law: I = I₀cos²(θ) where θ is the angle between polarization direction and analyzer transmission axis. Polarizer transmission: E' = E·cos(θ). Real-time visualization includes: (1) Three wave displays showing incident unpolarized/polarized light, light after first polarizer (linearly polarized), and light after second polarizer (analyzer) with transmitted intensity; (2) Intensity distribution graph plotting cos² function with current angle difference marked; (3) Polarizer system diagram showing light path through two polarizers with transmission axes. Adjustable parameters: polarizer 1 angle (0-180°), polarizer 2 angle (0-180°), initial polarization angle (0-180°), unpolarized/polarized source toggle, wave plate option with fast axis angle, animation speed, and display options (vectors, wave animation, intensity curve). Presets for parallel polarizers (max transmission), crossed polarizers (zero transmission), 45° difference (50% transmission), and auto-rotation demo. Wave plate mode demonstrates circular/elliptical polarization generation when linear polarization at 45° to fast axis. Educational content covers polarization mechanisms (Polaroid sheets, birefringent crystals, wire-grid polarizers), Malus's law derivation, wave plate retardation (quarter-wave and half-wave plates), polarization types (linear, circular, elliptical), and practical applications: sunglasses glare reduction, photography polarizing filters, LCD displays, photoelastic stress analysis, optical communications polarization multiplexing, astronomy magnetic field studies, 3D movies, and polarization microscopy. Multi-language support (zh, en, es, fr, de, ru, pt).
Young's Double Slit Interference - 杨氏双缝干涉
Interactive Young's double slit interference simulation demonstrating wave nature of light, superposition principle, and interference patterns. Features intensity formula: I(θ) = I₀·cos²(πd·sinθ/λ). Path difference: Δ = d·sinθ. Bright fringes (constructive interference) occur when d·sinθ = mλ (m = 0, ±1, ±2, ...). Dark fringes (destructive interference) occur when d·sinθ = (m+½)λ. Fringe spacing: Δx = λL/d. Real-time visualization includes: (1) Optical path diagram showing two slits separated by distance d, incident plane waves, interfering wavefronts from both slits, and screen with interference pattern; (2) Intensity distribution graph plotting cos² function with marked maxima positions (m = 0, ±1, ±2, ±3, ±4, ±5) and minima; (3) Simulated interference pattern showing bright and dark fringes on screen. Adjustable parameters: slit separation d (0.02-0.5 mm), screen distance L (0.1-5.0 m), wavelength λ (380-750 nm with color presets for blue 450nm, green 520nm, red 650nm), intensity scale, and display options (rays, maxima markers, minima markers). Presets for close slits (wide fringes), far slits (narrow fringes), red light (long λ), and blue light (short λ). Educational content covers wave superposition and interference mechanism, intensity distribution derivation from two-wave superposition, relationship between slit separation and fringe spacing (inverse proportionality Δx ∝ 1/d), wavelength dependence (red diffracts more than blue), and practical applications: measuring wavelength of light sources, determining small distances, studying coherence properties, wave-particle duality (electron double slit experiment), optical testing, and interferometric devices (Michelson interferometer, LIGO gravitational wave detector). Multi-language support (zh, en, es, fr, de, ru, pt).
Single Slit Diffraction - 单缝衍射
Interactive single slit diffraction simulation demonstrating wave spreading, interference patterns, and intensity distribution. Features intensity formula: I(θ) = I₀·[sin(β)/β]² where β = (πa·sinθ)/λ. Minima occur at a·sinθ = mλ (m = ±1, ±2, ...) creating dark fringes, while the central bright fringe has width Δx = 2λL/a. Real-time visualization includes: (1) Optical path diagram showing incident plane waves, narrow slit of width a, diffracted wavefronts spreading at various angles, and screen with intensity pattern; (2) Intensity distribution graph plotting sinc² function with marked minima positions (m = ±1, ±2, ±3) and maxima; (3) Simulated diffraction pattern showing realistic bright and dark fringes on screen. Adjustable parameters: slit width a (1-50 μm), screen distance L (0.1-5.0 m), wavelength λ (380-750 nm with color presets for blue 450nm, green 520nm, red 650nm), intensity scale, and display options (rays, minima markers, maxima markers). Presets for narrow slit (wide pattern), wide slit (narrow pattern), red light (long λ, wide pattern), blue light (short λ, narrow pattern). Educational content covers Huygens' principle and wavelet interference, intensity distribution derivation, sinc² function properties, relationship between slit width and pattern width (inverse proportionality), wavelength dependence on diffraction angle, and practical applications: measuring small objects (hair, wire) by analyzing diffraction pattern, determining unknown wavelengths, X-ray crystallography fundamentals, optical resolution limits (diffraction limit ≈ 1.22λ/D for circular apertures), and understanding wave-particle duality. Multi-language support (zh, en, es, fr, de, ru, pt).
Thin Film Interference - 薄膜干涉
Interactive thin film interference simulation demonstrating optical wave interference, phase shifts, and colorful fringe patterns. Features optical path difference formula: Δ = 2nd·cos(θ') + λ/2, where the λ/2 term represents the half-wave phase shift upon reflection from a denser medium (air-film interface). Constructive interference (bright fringes) occurs when Δ = mλ, destructive interference (dark fringes) when Δ = (m+½)λ. Snell's law: sin(θ) = n·sin(θ') calculates the refracted angle inside the film. Real-time visualization includes: (1) Optical path diagram showing incident ray, reflection from top surface, refraction into film, reflection from bottom surface, and exiting ray with proper angles; (2) Interference pattern canvas displaying thickness-dependent fringe intensity variations; (3) White light interference pattern showing colorful Newton's rings-style visualization with wavelength-dependent colors. Adjustable parameters: film thickness d (50-2000 nm), refractive index n (1.0-2.5), incident angle θ (0-89°), wavelength λ (380-750 nm with color presets for blue 450nm, green 520nm, red 650nm), light source type (monochrome, white light, laser), viewing angle, and display options (rays, normal line, labels). Material presets: soap bubble (n=1.33), oil film (n=1.45), glass plate (n=1.52), water film (n=1.33). Educational content covers interference mechanism, path difference derivation, white light dispersion explanation, and practical applications: anti-reflective coatings on lenses, dichroic filters, soap bubble colors, oil slick patterns, thickness measurement via ellipsometry, and structural color in nature (butterfly wings, peacock feathers, beetle shells). Multi-language support (zh, en, es, fr, de, ru, pt).
Doppler Effect - 多普勒效应
Interactive Doppler effect simulation demonstrating wave frequency changes due to relative motion between source and observer. Features Doppler formulas: f' = f₀·(v + vᵣ)/(v + vₛ) (general), f' = f₀·v/(v ± vₛ) (source motion), f' = f₀·(v ± vᵣ)/v (observer motion), where v = 343 m/s (speed of sound). Visual display includes wave source (S) and observer (O) on a 2D plane, animated wavefronts showing compression (blue, approaching) and rarefaction (red, receding), velocity vectors with magnitude labels, real-time frequency statistics (source frequency f₀, observed frequency f', frequency change Δf, ratio change %), and waveform comparison chart showing source vs observed waves. Adjustable parameters: source frequency f₀ (100-1000 Hz), source velocity vₛ (-150 to 150 m/s), source position xₛ, observer velocity vᵣ (-150 to 150 m/s), observer position xᵣ, wave speed v (100-500 m/s), wave amplitude, and animation speed. Scenario presets for stationary both, source approaching, source receding, observer approaching, and high speed source (supersonic effects). Display options include show/hide wavefronts, Doppler color map (blue/red gradient), and velocity vectors. Color coding: blue shift = higher frequency (approaching), red shift = lower frequency (receding). Applications in astronomy (redshift/blueshift for stellar velocities), radar speed detection, medical ultrasound Doppler imaging, emergency vehicle sirens, weather radar for wind patterns, and laser cooling in quantum physics. Multi-language support (zh, en, es, fr, de, ru, pt).
Sound Attenuation - 声强衰减
Interactive sound attenuation simulation demonstrating how sound intensity decreases with distance through two primary mechanisms: geometric spreading (inverse square law) and medium absorption. Features attenuation formulas: I = I₀/r² (geometric spreading in free field, where sound energy distributes over spherical surface area 4πr²), I = I₀·e^(-αx) (medium absorption, exponential decay with absorption coefficient α), I = I₀·e^(-αx)/r² (combined effect), and SPL = 10·log₁₀(I/I₀) (decibel conversion, logarithmic scale matching human hearing). Real-time visualization includes: animated circular wavefronts radiating from point source with color gradient indicating intensity (red=high, orange=medium, yellow=low, green=very low), interactive probe cursor for measuring intensity at any distance, dynamic decibel meter (0-120 dB range) with color-coded bar, real-time intensity display showing source intensity I₀, current distance, current intensity, and attenuation in dB, and comparison table listing intensity and sound level at distances 1-5m. Two operational modes: (1) Geometric Spreading mode demonstrating inverse square law with 6 dB drop per distance doubling, and (2) Medium Absorption mode showing exponential decay with adjustable absorption coefficient α (0.01-1.0 m⁻¹). Absorption presets for different media: Air (α=0.01), Water (α=0.05), Dense Medium (α=0.3). Adjustable parameters: source intensity I₀ (0.1-10.0 W/m²), absorption coefficient α (0.01-1.0 m⁻¹), max distance (3-10 m), and animation speed. Distance markers at 1m intervals with color-coded wavefronts. Educational content covering mathematical foundation with all four formulas, inverse square law explanation, absorption mechanisms in different media (air frequency-dependent absorption, water high-density absorption), real-world applications (concert hall design for even sound distribution, noise barrier engineering using attenuation calculations, audio engineering microphone placement, underwater acoustics sonar limitations, building acoustics reverberation and isolation), and human hearing perception (0 dB threshold at 1 kHz, 60 dB normal conversation, 120-140 dB pain threshold, logarithmic loudness perception where 10 dB increase sounds twice as loud, frequency-dependent sensitivity peaking at 3-4 kHz). Interactive canvas allows mouse movement to probe intensity at any point. Responsive design for all screen sizes. Multi-language support (zh, en, fr, de, es, pt, ru).
Rainbow Formation - 虹的形成可视化
Interactive rainbow formation visualization demonstrating the optical physics behind one of nature's most beautiful phenomena. Features rainbow physics equations: n₁sin(i) = n₂sin(r) (Snell's law for refraction), D = 180° - 2i + 4r (deviation angle for primary rainbow), D_min ≈ 42° (red light, n≈1.331), D_min ≈ 40° (violet light, n≈1.344). Real-time visualization with two complementary displays: Water Droplet Cross-Section showing the complete light path (incident ray enters from top-left, refracts into droplet at air-water interface, reflects internally at back surface, refracts again at exit point near bottom), and Observed Rainbow Arc showing the classic 40-42° rainbow as seen by observer with ROYGBIV spectrum from outer (red) to inner (violet). Light ray tracing with 7 spectrum colors (Red 700nm n=1.331, Orange 620nm n=1.332, Yellow 580nm n=1.333, Green 530nm n=1.335, Blue 470nm n=1.338, Indigo 420nm n=1.341, Violet 400nm n=1.344). Each color ray traced through the droplet showing different exit angles due to dispersion (violet bends more than red). White incident ray option to show light entering as white beam, spectrum colors option to show separated colored rays exiting droplet. Geometric optics calculation engine solving Snell's law in real-time: given incident angle i (0-90°) and refractive index n (1.0-1.5), calculate refraction angle r = arcsin(sin(i)/n), then deviation angle D = 180° - 2i + 4r. Adjustable parameters: incident angle i (0-90°, optimal ~59° for rainbow), refractive index n (1.0-1.5, water ~1.33, demonstrates how different media affect rainbow formation), droplet radius (50-150 px). Display options: show/hide normal lines (dashed reference lines perpendicular to surface), show angle arcs (visual angle measurement), show ray order (numbered 1-4 for incident, refracted, reflected, exit), animation speed control. Four preset scenarios: Primary Rainbow (standard 59° incidence, n=1.33), Alexander's Dark Band (50° incidence showing the dark region between primary and secondary rainbows), High Dispersion (exaggerated n=1.45 to dramatically show color separation), Custom Angle (45° for exploration). Real-time statistics display: incident angle i, refraction angle r, deviation angle D, and fixed rainbow angles (42° red, 40° violet). Educational content covering three-step rainbow formation process (refraction at entry, internal reflection, refraction at exit), why red appears outside and violet inside (different refractive indices create different exit angles), observation conditions (sun must be behind observer, rainbow centered on antisolar point at 40-42° from sun), secondary rainbow and Alexander's dark band (two internal reflections create fainter outer rainbow at 50-53° with reversed colors), and practical observation tips (lower sun = higher rainbow, best viewing during morning/evening, full circular rainbow visible from elevation). Mathematical foundation includes all four key equations. Multi-language support (zh, en, de, fr, es, ru, pt).
Beat Frequency Phenomenon - 拍音现象
Interactive beat frequency simulation with real audio output using Web Audio API demonstrating the acoustic beat phenomenon. Features wave equations: y₁ = A·sin(2πf₁t) (Tone 1), y₂ = A·sin(2πf₂t) (Tone 2), y = y₁ + y₂ (Superposition), beat frequency f_beat = |f₁ - f₂|. When two sound waves with slightly different frequencies interfere, they create amplitude modulation at the beat frequency - the characteristic 'wah-wah-wah' pulsating sound used in instrument tuning. Real-time waveform visualization: Tone 1 waveform (blue) showing individual sine wave at frequency f₁, Tone 2 waveform (red) showing individual sine wave at frequency f₂, Combined waveform (purple) displaying y₁ + y₂ superposition with audible beat pattern, Beat envelope visualization showing the amplitude modulation envelope (2A·cos(π·f_beat·t)) as dashed lines indicating maximum and minimum amplitude boundaries. Web Audio API implementation: Dual oscillator architecture with independent frequency control, master gain node for volume adjustment (0-100%), real-time frequency updates while audio is playing, analyser node for audio visualization. Adjustable parameters: Tone 1 frequency f₁ (200-800 Hz, default 440 Hz - A4), Tone 2 frequency f₂ (200-800 Hz, default 444 Hz), master volume control, wave type selection (sine, triangle, square). Automatic note name display with cent deviation (e.g., 'A4 + 4¢' for 444 Hz). Real-time beat statistics: beat frequency f_beat = |f₁ - f₂| in Hz, beat period T_beat = 1/f_beat in seconds, beats per second count. Quick presets: Slow Beat (2 Hz, f₁=440, f₂=442), Moderate (4 Hz, f₁=440, f₂=444), Fast Beat (8 Hz, f₁=440, f₂=448), Tuning Fork (440+442 Hz), Unison/No Beat (440+440 Hz). Educational content: mathematical foundation with all four formulas, real-world applications (instrument tuning by listening for beat disappearance, piano tuning with beat rate intervals, Doppler radar velocity measurement, music production synth detuning techniques, heterodyne radio detection), listening guide with tips for slow beats (2-4 Hz for clear wah-wah), envelope focus (amplitude modulation perception), and fast beat merging (>15 Hz creates difference tone perception). Playback controls with play/stop buttons and responsive canvas rendering for all screen sizes. Multi-language support (zh, en, es, fr, de, ru, pt, ja).
Sonar Principle - 声呐原理可视化
Interactive sonar principle simulation demonstrating underwater sound navigation and ranging. Features sonar equations: t = 2d/v (round trip time), d = v·t/2 (distance calculation), λ = v/f (wavelength), T = 1/f (period). Active sonar operation showing sound pulse (ping) transmission through water at ~1500 m/s, wave reflection from targets, echo detection and distance calculation. Real-time visualization with two main displays: Sonar Display (top-down underwater view) showing boat with transducer, circular wavefronts expanding outward, target detection with echo indication, and range rings (100m, 200m, 300m, 400m, 500m); Signal Strength Display showing signal attenuation curve over distance based on inverse square law and absorption loss, with echo pulse markers when targets are detected. Target system with configurable parameters: 1-5 simultaneous targets, adjustable distance (50-2000m), target size (10-200m), random positioning with angular distribution. Sound parameters: sound speed v (1000-2000 m/s, simulating temperature/salinity effects), frequency f (10-200 kHz, affecting resolution vs range trade-off), transmit power (10-100%). Wavefront animation showing circular acoustic pulses expanding at realistic speed scaled to sound velocity, with alpha fading as energy dissipates. Echo detection system triggers when wavefront intersects target, displaying distance label and detection indicator. Real-time statistics: detected target count, closest distance with decimal precision, round-trip time calculation. Four preset scenarios: Shallow Water (high frequency 200kHz, 100m range, small target), Deep Water (low frequency 20kHz, 1500m range, large target), Multiple Targets (4 targets at 500m), Submarine Detection (1530 m/s sound speed, 800m range, 80m target). Display options: show/hide wavefronts, echo pulses, targets; animation speed control (0.1x-3.0x). Playback controls: Start (continuous animation), Pause, Reset, Send Ping (manual pulse transmission). Educational content covering sonar principles, active vs passive sonar, echo location physics, applications (navigation, bathymetry, fish finding, submarine detection, underwater archaeology, oceanographic research), and factors affecting performance (temperature, salinity, depth, frequency choice, target characteristics, background noise, refraction shadow zones). Multi-language support (zh, en, de, fr, es, ru, pt).
Standing Wave - 驻波可视化
Interactive standing wave simulation showing nodes, antinodes, and harmonic frequencies. Features standing wave equations: y₁ = Asin(kx - ωt) (incident wave), y₂ = Asin(kx + ωt) (reflected wave), y = y₁ + y₂ = 2Asin(kx)cos(ωt) (standing wave). Nodes occur at sin(kx) = 0 → x = nλ/2 (zero displacement points), antinodes at |sin(kx)| = 1 → x = (2n+1)λ/4 (maximum amplitude points). Real-time visualization of three wave displays: Incident wave (blue) traveling right, Reflected wave (red) traveling left, and Standing wave (purple) showing the superposition with envelope. Split-screen display shows how incident and reflected waves combine to form standing wave pattern. Adjustable parameters: string length L (0.5-5.0 m), harmonic number n (1-10), frequency f (0.1-10 Hz), amplitude A (0.1-2.0), wave speed v (0.5-5.0 m/s), and animation speed. Harmonic presets for fundamental (1st), 2nd, 3rd, 4th, and 5th harmonics. Display options include show nodes (green markers), show antinodes (orange markers), show envelope, and resolution control. Real-time statistics display node count, antinode count, and wavelength λ = v/f. Applications in musical instruments (guitar strings, wind instruments, organ pipes) demonstrating resonance and harmonics; string vibration physics; acoustics and room modes; quantum mechanics (particle in a box as standing matter wave); and architectural acoustics. Multi-language support (zh, en, es, fr, de, ru, pt).
Wave Superposition - 波的叠加
Interactive wave superposition simulation demonstrating wave interference, beat frequency, and superposition principle. Features wave equations: y₁ = A₁sin(kx - ωt + φ₁), y₂ = A₂sin(kx - ωt + φ₂), superposition y = y₁ + y₂, beat frequency f_beat = |f₁ - f₂|, and angular frequency ω = 2πf. Real-time visualization of three wave displays: Wave 1 (blue) with adjustable frequency f₁ (0.5-10 Hz), amplitude A₁ (0.1-2.0), and phase φ₁ (0-2π); Wave 2 (red) with adjustable frequency f₂ (0.5-10 Hz), amplitude A₂ (0.1-2.0), and phase φ₂ (0-2π); Superposition wave (purple) showing y₁ + y₂ with beat envelope visualization. Beat indicator detects and displays beat pattern when |f₁ - f₂| < 1 Hz with pulsing animation. Charts include amplitude at x=0 over time, phase difference between waves, and wave energy (proportional to amplitude squared). Presets for perfect constructive interference (f₁=f₂, φ₁=φ₂), perfect destructive interference (f₁=f₂, φ₁-φ₂=π), beat pattern (f₁≈f₂), and octave harmonic (f₂=2f₁). Display options include wave speed control, resolution adjustment, beat envelope toggle, and displacement vectors toggle. Applications in acoustics (musical beats, instrument tuning), optics (interference patterns, thin film colors), quantum mechanics (wave function superposition), and communication systems (signal modulation, noise cancellation). Multi-language support (zh, en, es, fr, de, ru, pt).