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Acoustics operators

22 operators in the acoustics category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
AC1Speed of sound in a medium derived from the ratio of bulk modulus to density, corrected by Laplace for adiabatic conditions.v = \sqrt{\frac{B}{\rho}}
AC2Standing wave harmonic frequencies in a tube or string of length L, giving the nth resonant frequency from wave speed and mode number.f_n = \frac{n v}{2L}
AC3Doppler effect formula predicting the observed frequency shift when a sound source and observer are in relative motion.f\prime = f\frac{v \pm v_o}{v \mp v_s}
AC4Sound intensity from a point source decreasing with the inverse square of distance as power spreads over a spherical wavefront.I = \frac{P}{4\pi r^2}
AC5Decibel scale expressing sound intensity level as ten times the logarithm of the intensity ratio relative to the hearing threshold.\beta = 10\log_{10}\frac{I}{I_0}
AC6Beat frequency produced by the superposition of two tones with slightly different frequencies, equal to their absolute difference.f_{beat} = |f_1 - f_2|
AC7Fundamental wavelength-frequency relation linking the spatial period of a wave to its temporal frequency and propagation speed.\lambda = \frac{v}{f}
ACX1Acoustic wave equation governing pressure disturbance propagation in a homogeneous medium as a second-order partial differential equation.\frac{\partial^2 p}{\partial t^2} = c^2\nabla^2 p
ACX10Converts sound power level to sound pressure level at a given distance assuming spherical spreading from a point source.L_p = L_w - 10\log_{10}(4\pi r^2)
ACX11Fundamental resonant frequency of an open or closed pipe determined by the ratio of sound speed to twice the tube length.f_r = \frac{c}{2L}
ACX12Nth harmonic resonant frequency of a resonator, extending the fundamental mode to integer multiples for standing wave analysis.f_n = \frac{nc}{2L}
ACX13Quality factor of a resonant system defined as the center frequency divided by the half-power bandwidth, measuring resonance sharpness.Q = \frac{f_0}{\Delta f}
ACX14Stokes acoustic absorption coefficient quantifying viscous dissipation of sound energy proportional to frequency squared in a fluid medium.\alpha = \frac{2\eta\omega^2}{3\rho c^3}
ACX15Acoustic wavelength as the ratio of sound speed to frequency, giving the spatial period of a propagating sound wave.\lambda = \frac{c}{f}
ACX2Acoustic intensity expressed as the squared pressure amplitude divided by the product of medium density and sound speed.I = \frac{p^2}{\rho c}
ACX3Characteristic acoustic impedance of a medium defined as the product of its density and sound speed, governing wave transmission behavior.Z = \rho c
ACX4Acoustic reflection coefficient quantifying the fraction of incident wave energy reflected at an impedance discontinuity between two media.R = \left(\frac{Z_2 - Z_1}{Z_2 + Z_1}\right)^2
ACX5Acoustic transmission coefficient giving the fraction of incident wave energy transmitted through an interface, complementary to reflection.T = 1 - R = \frac{4Z_1 Z_2}{(Z_1 + Z_2)^2}
ACX6Transmission loss in decibels measuring the sound attenuation through a barrier or interface from the inverse of the transmission coefficient.TL = 10\log_{10}\frac{1}{T}
ACX7Sabine reverberation time predicting how long sound persists in an enclosed space from room volume and total absorption area.RT_{60} = \frac{0.161 V}{A}
ACX8Total sound absorption area in a room computed by summing the products of each surface area and its absorption coefficient.A = \sum_i S_i\alpha_i
ACX9Sound pressure level in decibels referencing measured pressure to the standard hearing threshold of 20 micropascals.SPL = 20\log_{10}\frac{p}{p_{ref}}

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["AC1"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​