Sound Intensity Calculator — calculate sound intensity with the correct physics formula. Worked example and unit notes included.
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.
Compare Amplitude Calculator, Sound Decibels Calculator, and Frequency Calculator when the same physical system crosses between related topics. These companions help connect the input variables, but they do not make the underlying model interchangeable: keep the measured quantity, unit convention, reference direction, and material or medium beside every result.
Wave quantities are linked but not interchangeable: frequency describes cycles per second, wavelength describes distance per cycle, amplitude describes the size of the oscillation, and intensity or decibel level describes how energy is observed. Optics and acoustics also depend on the medium, so keep the propagation speed and boundary conditions explicit when comparing a classroom estimate with a measured signal.
Physics estimates remain conditional on their assumptions. Decide whether the problem uses an ideal wave, a point mass, a rigid body, a steady flow, a reversible cycle, or a quantum approximation before entering values. State temperature, pressure, geometry, boundary conditions, and significant figures with the output so another reader can reproduce the calculation and judge whether the result is useful.
A simple sanity check should accompany any important result: inspect the dimensions, vary one input at a time, and confirm that the direction of change matches the governing equation. A plausible number is not enough if a wavelength, force, energy, momentum, or temperature was entered in the wrong unit or with the wrong sign convention.
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.
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.
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.