🎛️ Controls

• Wave 1 Frequency: Adjust from 1.0 to 20.0 Hz
• Wave 2 Frequency: Adjust from 1.0 to 20.0 Hz
• Wave 2 Phase: Shift the phase from 0° to 360°

📊 What You Can Observe

• Beat Patterns: When frequencies are close, you'll see slow amplitude modulation in the sum wave
• Constructive Interference: Waves align to create maximum amplitude
• Destructive Interference: Waves cancel each other out
• Harmonic Relationships: Integer frequency ratios create stable, repeating patterns
• Complex Interference: Non-integer ratios produce evolving, complex patterns
• Phase Effects: How shifting one wave affects the combined result

🎵 Interesting Combinations to Try

🔬 Educational Applications

• Physics: Wave interference, superposition principle, standing waves
• Acoustics: Beat frequencies, musical intervals, sound wave interactions
• Signal Processing: Frequency mixing, modulation effects, spectrum analysis
• Mathematics: Trigonometric functions, periodic behavior, harmonic analysis

💡 Tips for Exploration

• Start with identical frequencies and adjust phase to see interference effects
• Gradually change one frequency to observe the transition from interference to beats
• Try simple integer ratios (1:2, 2:3, 3:4) to see harmonic relationships
• Observe how the difference wave shows beating more clearly than the sum
• Use small frequency differences (0.1-0.5 Hz) to create slow, visible beats