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PhysicsSimple harmonic motion and period

Linear restoring acceleration produces sinusoidal motion.

Model PhysicsSimple pendulum and the small-angle limit

The familiar pendulum period requires a small swing.

Model PhysicsAmplitude, phase, wavelength and polarization direction

A wave’s pattern speed differs from the motion of its medium.

Model PhysicsEnergy carried by a sinusoidal string wave

Energy transport grows with squared amplitude and frequency in the linear model.

Model PhysicsSound intensity and decibel level

A decibel value needs a reference and a specified measured quantity.

Model PhysicsBeats from nearby frequencies

Slow modulation comes from superposing close frequencies.

Model PhysicsAcoustic Doppler shift in a medium

Source and observer velocities are measured relative to the medium.

Model Physics · ChemistryHeat, temperature and specific heat

Heat is energy transferred because of a temperature difference.

Model PhysicsThermal expansion coefficients

Thermal size changes depend on temperature and constraints.

Model Physics · ChemistryPressure–volume work and process paths

Boundary work depends on the process, while internal energy is a state function.

Model Physics · ChemistryReversible adiabatic ideal-gas relations

The power law needs an ideal gas and constant heat-capacity ratio.

Model Physics · ChemistryReversible and quasistatic processes

Restoring the system alone does not establish reversibility.

Model Physics · ChemistryEntropy change and reversible heat transfer

Use a reversible comparison path to calculate a state-function change.

Model PhysicsRefrigerator and heat-pump performance

A heat pump moves heat as well as consuming work.

Model Physics · ChemistryMean free path in a dilute hard-sphere gas

A collision length depends on number density and cross section.

Model PhysicsAtomic net charge and electrical neutrality

Neutral matter can contain both positive and negative charge.

Model PhysicsConductors, insulators and electrostatic induction

Charge mobility and polarization are different from net charging.

Model PhysicsConductors in electrostatic equilibrium

Equilibrium field vanishes in the conducting material, including a charged conductor.

Model PhysicsElectric potential, voltage and potential energy

Voltage is energy change per unit charge.

Model PhysicsCurrent density and carrier drift

Current measures signed charge flow across a surface.

Model PhysicsResistance, resistivity and conductor geometry

Resistance belongs to a device geometry; resistivity is a material response.

Model PhysicsSeries and parallel resistor networks

Series shares current; parallel shares voltage.

Model PhysicsElectrical power and Joule heating

Voltage times signed current measures element power.

Model PhysicsElectromotive force and terminal voltage

An emf is an energy-per-charge quantity, not a force.

Model PhysicsSeries and parallel capacitor networks

Capacitor network rules differ from resistor rules.

Model PhysicsEnergy stored in a linear capacitor

Charging work produces electric-field energy.

Model PhysicsMagnetic flux and Faraday–Lenz induction

Induction responds to flux change, not simply to the presence of a magnetic field.

Model PhysicsEnergy stored in a linear inductor

Inductive storage and resistive loss are separate.

Model PhysicsMagnetic fields of a straight wire and circular loop

Field geometry follows the current distribution.

Model PhysicsIdeal transformer voltage and current ratios

Turns change voltage and current while conserving ideal power.

ModelSource checked

Sound intensity and decibel level

Physics

A decibel value needs a reference and a specified measured quantity.

Key knowledge

Sound intensity is average acoustic energy flux per area. A progressive sinusoidal plane wave in a lossless fluid has I=p_peak²/(2ρc_s)=p_rms²/(ρc_s). Sound intensity level is L_I=10log₁₀(I/I_ref), commonly with I_ref=10⁻¹² W m⁻². A tenfold intensity increase is 10 dB; intensity level, sound-pressure level and perceived loudness are distinct.

Values and equations

I=p_peak²/(2ρc_s)=p_rms²/(ρc_s); L_I=10log₁₀(I/I_ref)

I,I_ref: Acoustic intensity and positive reference intensity W m⁻²
p_peak,p_rms: Peak and rms pressure fluctuations Pa
ρ: Equilibrium fluid density kg m⁻³
c_s: Sound speed m s⁻¹
L_I: Intensity level dB

Conditions and scope

Linear progressive plane wave, stated averaging interval, fluid density ρ>0 and sound speed c_s>0; p_peak is the pressure-fluctuation amplitude and p_rms=p_peak/√2 for a sinusoid.
The level requires I>0 and I_ref>0. Standing waves/near fields do not generally satisfy the progressive-wave intensity–pressure relation; the reference is a convention, not a universal hearing threshold.

Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

University Physics Volume 1, §17.3: sound intensitySamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §17.3 intensity17.8, sinusoidal pressure/intensity17.11 and level17.12. RMS relation is the sinusoidal mean-square identity; exclude universal hearing-threshold and universal loudness claims.

2026-10-10 · /root/audit_life_earth_chemistry — independent Chemistry/Life/Earth editor. Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

Entry details

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Record identity: foundation-physics-sound-intensity-level
Revision: foundations-refresh.1
Structured reference record: Foundational reference additions