Amplitude Calculator

A physics wave calculator covers three interconnected areas of wave physics: wave mechanics (speed, frequency, wavelength, period), optics (Snell's law of refraction, thin lens equation, magnification, critical angle for total internal reflection), and room acoustics (sound pressure level at distance, reverberation time via the Sabine formula). These topics span physics curricula from GCSE to university level and have wide practical applications — from optical fibre design to concert hall acoustics.

Wave speed, frequency, and wavelength are linked by v = fλ. In air at 20 °C, sound travels at ~343 m/s; light travels at ~3 × 10⁸ m/s in a vacuum. The period T = 1/f tells you how long each cycle takes. Optics calculations use Snell's law (n₁ sin θ₁ = n₂ sin θ₂) and the thin lens formula (1/v − 1/u = 1/f). Acoustics calculations use the inverse square law for SPL and Sabine's RT60 formula for room reverberation.

1. Wave Speed tab: enter frequency (Hz) and wavelength (m) to compute wave speed and period.
2. Optics tab: enter refractive indices n₁ and n₂ and the angle of incidence to find the refracted angle (Snell's law) and critical angle for total internal reflection. Enter focal length and object distance to compute image distance and magnification.
3. Acoustics tab: enter source SPL at 1 m and measurement distance to get the SPL at that distance. Enter room dimensions and average absorption coefficient to compute RT60 using Sabine's formula.

Wave physics formulas

Wave speed: v = fλ. Period T = 1/f. For electromagnetic waves in vacuum: v = c = 2.998 × 10⁸ m/s.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂. Critical angle θ_c = arcsin(n₂/n₁) when n₁ > n₂. Thin lens: 1/v − 1/u = 1/f; magnification m = −v/u.

Inverse square law (SPL): L₂ = L₁ − 20 log₁₀(r₂/r₁). Sabine RT60: T₆₀ = 0.161 V / (α S), where V = room volume (m³), S = total surface area (m²), α = average absorption coefficient.

Interpreting wave calculator results

RT60 targets for different spaces

Ideal RT60 for speech intelligibility is 0.4–0.8 s. Music venues target 1.5–2.5 s for orchestral music and 0.8–1.2 s for chamber music. Home theatre rooms target 0.3–0.5 s. Higher absorption coefficients (soft furnishings, acoustic panels) reduce RT60; hard surfaces (concrete, glass) increase it. OSHA limits workplace noise to 85 dB(A) over an 8-hour exposure; each 5 dB increase halves the permissible exposure time.

Physics tips and best practices

• Frequency in Hz must be positive and non-zero — wavelength and wave speed depend on division by frequency.
• Snell's law only predicts a refracted ray when sin θ₂ ≤ 1. Beyond the critical angle (from a denser to a less dense medium), total internal reflection occurs — no transmitted ray exists. This is the principle behind optical fibres.
• The thin lens formula assumes a thin, paraxial approximation. Real thick lenses and wide-angle systems require more complex models.
• Sabine's formula overestimates RT60 in highly absorptive rooms (α > 0.3). The Eyring formula (−0.161V / S·ln(1−α)) gives better results for those cases.

Wave, optics, and acoustics formulas are standard physics relations derived from Maxwell's equations, geometric optics, and linear acoustics theory. Snell's law and the thin lens equation assume ideal, homogeneous media and paraxial conditions. Acoustic calculations use Sabine's approximation. This calculator is for educational and estimation purposes only.

Related Calculators

• Speed Calculator
• Force Calculator
• Kinetic Energy Calculator
• Potential Energy Calculator