Waves

Calculate wavelength, frequency, amplitude, and wave velocity.

Analyze frequency shifts due to relative motion of source and observer.

Analyze constructive and destructive interference patterns between two waves with interactive visualization.

Analyze standing wave patterns, nodes, antinodes, and resonance frequencies.

Calculate reflection coefficients, phase shifts, and energy transfer at boundaries.

Analyze wave transmission between different media and wavelength changes.

Study single slit diffraction patterns and interference minima.

Analyze resonance phenomena, amplitude amplification, and damping effects.

Calculate image formation by thin lenses using the lens equation and ray tracing.

Calculate wave speed, wavelength, and frequency relationships for different wave types.

Calculate beat frequency from two superposing waves: f_beat = |f₁ − f₂|.

Convert sound intensity to decibels using β = 10 log₁₀(I/I₀).

Find fundamental frequency of a string fixed at both ends: f₁ = v/(2L).

Resonant frequencies of an open organ pipe: fₙ = nv/(2L).

Resonant frequencies of a closed pipe (odd harmonics): fₙ = nv/(4L).

Calculate power transported by a sound wave: P = ½ρω²A²v.

Find phase difference from path difference: Δφ = 2πΔx/λ.

Intensity decay in absorbing media: I = I₀e^(−αx).

Compare object speed to sound speed: Ma = v/vₛ.

Resultant amplitude when two waves superpose with phase difference.