Logarithmic unit measuring sound pressure level

dB SPL (Sound Pressure Level) measures sound pressure relative to 20 µPa, the threshold of human hearing. The logarithmic scale means +10 dB = 10× pressure increase, +20 dB = 100× pressure increase, but only 2× perceived loudness due to human hearing nonlinearity.

Example: Conversation at 60 dB has 1000× more pressure than hearing threshold at 0 dB, but sounds only 16× louder subjectively.

Physical force per area exerted by sound waves

Sound pressure is the instantaneous pressure variation caused by a sound wave, measured in pascals (Pa). It varies from 20 µPa (barely audible) to 200 Pa (painfully loud). The RMS (root mean square) pressure is typically reported for continuous sounds.

Example: Normal speech creates 0.02 Pa (63 dB). A rock concert reaches 2 Pa (100 dB)—100× higher pressure but only 6× louder perceptually.

Acoustic power per unit area

Sound intensity measures acoustic energy flow through a surface, in watts per square meter. It relates to pressure² and is fundamental in calculating sound power. The threshold of hearing is 10⁻¹² W/m², while a jet engine produces 1 W/m² at close range.

Example: Whisper has 10⁻¹⁰ W/m² intensity (20 dB). Threshold of pain is 1 W/m² (120 dB)—1 trillion times more intense.

Phonograph Invented

Thomas Edison invents the phonograph, enabling the first recordings and playback of sound, sparking interest in quantifying audio levels.

Decibel Introduced

Bell Telephone Laboratories introduces the decibel for measuring transmission loss in telephone cables. Named after Alexander Graham Bell, it quickly becomes standard for audio measurement.

Fletcher-Munson Curves

Harvey Fletcher and Wilden A. Munson publish equal-loudness contours showing frequency-dependent hearing sensitivity, laying groundwork for A-weighting and phon scale.

Sound Level Meter

First commercial sound level meter developed, standardizing noise measurement for industrial and environmental applications.

Sone Scale Standardized

Stanley Smith Stevens formalizes the sone scale (ISO 532), providing a linear measure of perceived loudness where doubling sones = doubling perceived loudness.

OSHA Standards

US Occupational Safety and Health Administration establishes noise exposure limits (85-90 dB TWA), making sound measurement critical for workplace safety.

ISO 226 Revision

Updated equal-loudness contours based on modern research, refining phon measurements and A-weighting accuracy across frequencies.

Digital Audio Standards

LUFS (Loudness Units relative to Full Scale) standardized for broadcast and streaming, replacing peak-only measurements with perceptually-based loudness metering.

• **+3 dB = doubling power** (barely noticeable to most people)
• **+6 dB = doubling pressure** (inverse square law, halving distance)
• **+10 dB ≈ 2× louder** (perceived loudness doubles)
• **+20 dB = 10× pressure** (two decades on log scale)
• **60 dB SPL ≈ normal conversation** (at 1 meter distance)
• **85 dB = OSHA 8-hour limit** (hearing protection threshold)
• **120 dB = threshold of pain** (immediate discomfort)

• **Equal sources:** 80 dB + 80 dB = 83 dB (not 160!)
• **10 dB apart:** 90 dB + 80 dB ≈ 90.4 dB (quieter source barely matters)
• **20 dB apart:** 90 dB + 70 dB ≈ 90.04 dB (negligible contribution)
• **Doubling sources:** N equal sources = original + 10×log₁₀(N) dB
• **10 equal 80 dB sources = 90 dB total** (not 800 dB!)

• **0 dB SPL** = 20 µPa = threshold of hearing
• **20 dB** = whisper, quiet library
• **60 dB** = normal conversation, office
• **85 dB** = heavy traffic, hearing risk
• **100 dB** = nightclub, chainsaw
• **120 dB** = rock concert, thunder
• **140 dB** = gunshot, jet engine nearby
• **194 dB** = theoretical max in atmosphere

• **Never add dB arithmetically** — use logarithmic addition formulas
• **dBA ≠ dB SPL** — A-weighting reduces bass, no direct conversion possible
• **Distance doubling** ≠ half the level (it's -6 dB, not -50%)
• **3 dB barely noticeable,** not 3× louder — perception is logarithmic
• **0 dB ≠ silence** — it's the reference point (20 µPa), can go negative
• **phon ≠ dB** except at 1 kHz — frequency-dependent equal loudness

Three reasons make logarithmic measurement essential:

• Human perception: Ears respond logarithmically—doubling pressure sounds like +6 dB, not 2×
• Range compression: 0-140 dB vs 20 µPa - 200 Pa (impractical for daily use)
• Multiplication becomes addition: Combining sound sources uses simple addition
• Natural scaling: Factors of 10 become equal steps (20 dB, 30 dB, 40 dB...)

The logarithmic scale is counterintuitive. Avoid these errors:

• 60 dB + 60 dB = 63 dB (not 120 dB!) — logarithmic addition
• 90 dB - 80 dB ≠ 10 dB difference—subtract values, then antilog
• Doubling distance reduces level by 6 dB (not 50%)
• Halving power = -3 dB (not -50%)
• 3 dB increase = 2× power (barely noticeable), 10 dB = 2× loudness (clearly audible)

Core equations for sound level calculations:

• Pressure: dB SPL = 20 × log₁₀(P / 20µPa)
• Intensity: dB IL = 10 × log₁₀(I / 10⁻¹²W/m²)
• Power: dB SWL = 10 × log₁₀(W / 10⁻¹²W)
• Combining equal sources: L_total = L + 10×log₁₀(n), where n = number of sources
• Distance law: L₂ = L₁ - 20×log₁₀(r₂/r₁) for point sources

You cannot add decibels arithmetically. Use logarithmic addition:

• Two equal sources: L_total = L_single + 3 dB (e.g., 80 dB + 80 dB = 83 dB)
• Ten equal sources: L_total = L_single + 10 dB
• Different levels: Convert to linear, add, convert back (complex)
• Rule of thumb: Adding sources 10+ dB apart barely increases total (<0.5 dB)
• Example: 90 dB machine + 70 dB background = 90.04 dB (barely noticeable)

Unit of loudness level referenced to 1 kHz

Phon values follow equal-loudness contours (ISO 226:2003). A sound at N phons has the same perceived loudness as N dB SPL at 1 kHz. At 1 kHz, phon = dB SPL exactly. At other frequencies, they differ dramatically due to ear sensitivity.

• 1 kHz reference: 60 phon = 60 dB SPL at 1 kHz (by definition)
• 100 Hz: 60 phon ≈ 70 dB SPL (+10 dB needed for equal loudness)
• 50 Hz: 60 phon ≈ 80 dB SPL (+20 dB needed—bass sounds quieter)
• 4 kHz: 60 phon ≈ 55 dB SPL (-5 dB—peak ear sensitivity)
• Application: Audio equalization, hearing aid calibration, sound quality assessment
• Limitation: Frequency-dependent; requires pure tones or spectrum analysis

Linear unit of subjective loudness

Sones quantify perceived loudness linearly: 2 sones sounds twice as loud as 1 sone. Defined by Stevens' power law, 1 sone = 40 phon. Doubling sones = +10 phon = +10 dB at 1 kHz.

• 1 sone = 40 phon = 40 dB SPL at 1 kHz (definition)
• Doubling: 2 sones = 50 phon, 4 sones = 60 phon, 8 sones = 70 phon
• Stevens' law: Perceived loudness ∝ (intensity)^0.3 for mid-level sounds
• Real-world: Conversation (1 sone), vacuum (4 sones), chainsaw (64 sones)
• Application: Product noise ratings, appliance comparisons, subjective assessment
• Advantage: Intuitive—4 sones literally sounds 4× louder than 1 sone

Professional audio uses dB extensively for signal levels, mixing, and mastering:

• 0 dBFS (Full Scale): Maximum digital level before clipping
• Mixing: Target -6 to -3 dBFS peak, -12 to -9 dBFS RMS for headroom
• Mastering: -14 LUFS (loudness units) for streaming, -9 LUFS for radio
• Signal-to-noise ratio: >90 dB for professional equipment, >100 dB for audiophile
• Dynamic range: Classical music 60+ dB, pop music 6-12 dB (loudness war)
• Room acoustics: RT60 reverberation time, -3 dB vs -6 dB roll-off points

Workplace noise exposure limits prevent hearing loss:

• OSHA: 85 dB = 8-hour TWA (time-weighted average) action level
• 90 dB: 8 hours max exposure without protection
• 95 dB: 4 hours max, 100 dB: 2 hours, 105 dB: 1 hour (halving rule)
• 115 dB: 15 minutes max without protection
• 140 dB: Immediate danger—hearing protection mandatory
• Dosimetry: Cumulative exposure tracking using noise dosimeters

Environmental regulations protect public health and quality of life:

• WHO guidelines: <55 dB daytime, <40 dB nighttime outdoors
• EPA: Ldn (day-night average) <70 dB to prevent hearing loss
• Aircraft: FAA requires noise contours for airports (65 dB DNL limit)
• Construction: Local limits typically 80-90 dB at property line
• Traffic: Highway noise barriers target 10-15 dB reduction
• Measurement: dBA weighting approximates human annoyance response

Acoustic design requires precise sound level control:

• Speech intelligibility: Target 65-70 dB at listener, <35 dB background
• Concert halls: 80-95 dB peak, 2-2.5s reverberation time
• Recording studios: NC 15-20 (noise criterion curves), <25 dB ambient
• Classrooms: <35 dB background, 15+ dB speech-to-noise ratio
• STC ratings: Sound Transmission Class (wall isolation performance)
• NRC: Noise Reduction Coefficient for absorption materials

• Use calibrated Class 1 or Class 2 sound level meters (IEC 61672)
• Calibrate before each session with acoustic calibrator (94 or 114 dB)
• Position microphone away from reflective surfaces (1.2-1.5m height typical)
• Use slow response (1s) for steady sounds, fast (125ms) for fluctuating
• Apply windscreen outdoors (wind noise starts at 12 mph / 5 m/s)
• Record for 15+ minutes to capture temporal variations

• A-weighting (dBA): General purpose, environmental, occupational noise
• C-weighting (dBC): Peak measurements, low-frequency assessment
• Z-weighting (dBZ): Flat response for full-spectrum analysis
• Never convert dBA ↔ dBC—frequency content dependent
• A-weighting approximates 40-phon contour (moderate loudness)
• Use octave-band analysis for detailed frequency information

• Always specify: dB SPL, dBA, dBC, dBZ (never just 'dB')
• Report time weighting: Fast, Slow, Impulse
• Include distance, measurement height, and orientation
• Note background noise levels separately
• Report Leq (equivalent continuous level) for varying sounds
• Include measurement uncertainty (±1-2 dB typical)

• 85 dB: Consider protection for prolonged exposure (>8 hours)
• 90 dB: Mandatory protection after 8 hours (OSHA)
• 100 dB: Use protection after 2 hours
• 110 dB: Protect after 30 minutes, double protection above 115 dB
• Earplugs: 15-30 dB reduction, earmuffs: 20-35 dB
• Never exceed 140 dB even with protection—physical trauma risk

Blue whales produce calls up to 188 dB SPL underwater—the loudest biological sound on Earth. These low-frequency calls (15-20 Hz) can travel hundreds of miles through the ocean, enabling whale communication across vast distances.

The world's quietest room (Microsoft, Redmond) measures -20.6 dB SPL—quieter than the threshold of hearing. People can hear their own heartbeat, blood circulation, and even stomach gurgling. No one has stayed more than 45 minutes due to disorientation.

The loudest sound in recorded history: 310 dB SPL at source, heard 3,000 miles away. The pressure wave circled Earth 4 times. Sailors 40 miles away suffered ruptured eardrums. Such intensity cannot exist in normal atmosphere—creates shock waves.

194 dB SPL is the theoretical maximum in Earth's atmosphere at sea level—beyond this, you create a shock wave (explosion), not a sound wave. At 194 dB, rarefaction equals vacuum (0 Pa), so sound becomes discontinuous.

Dogs hear 67-45,000 Hz (vs humans 20-20,000 Hz) and detect sounds 4× farther away. Their hearing sensitivity peaks around 8 kHz—10 dB more sensitive than humans. This is why dog whistles work: 23-54 kHz, inaudible to humans.

Movie theaters target 85 dB SPL average (Leq) with 105 dB peaks (Dolby spec). This is 20 dB louder than home viewing. Extended low-frequency response: 20 Hz subwoofers enable realistic explosions and impacts—home systems typically cut off at 40-50 Hz.

dBA applies frequency-dependent weighting that attenuates low frequencies. A 100 Hz tone at 80 dB SPL measures ~70 dBA (-10 dB weighting), while 1 kHz at 80 dB SPL measures 80 dBA (no weighting). Without knowing the frequency spectrum, conversion is impossible. You'd need FFT analysis and apply the inverse A-weighting curve.

+3 dB = doubling power or intensity, but only 1.4× pressure increase. Human perception follows logarithmic response: 10 dB increase sounds roughly 2× louder. 3 dB is the smallest change most people detect under controlled conditions; in real environments, 5+ dB is needed.

You cannot add decibels arithmetically. For equal levels: L_total = L + 3 dB. For different levels: Convert to linear (10^(dB/10)), add, convert back (10×log₁₀). Example: 80 dB + 80 dB = 83 dB (not 160 dB!). Rule of thumb: source 10+ dB quieter contributes <0.5 dB to total.

dB SPL: Unweighted sound pressure level. dBA: A-weighted (approximates human hearing, attenuates bass). dBC: C-weighted (nearly flat, minimal filtering). Use dBA for general noise, environmental, occupational. Use dBC for peak measurements and low-frequency assessment. They measure the same sound differently—no direct conversion.

Sound follows inverse-square law: doubling distance reduces intensity by ¼ (not ½). In dB: every doubling of distance = -6 dB. Example: 90 dB at 1m becomes 84 dB at 2m, 78 dB at 4m, 72 dB at 8m. This assumes point source in free field—rooms have reflections that complicate this.

Yes! 0 dB SPL is the reference point (20 µPa), not silence. Negative dB means quieter than reference. Example: -10 dB SPL = 6.3 µPa. Anechoic chambers measure down to -20 dB. However, thermal noise (molecular motion) sets absolute limit around -23 dB at room temperature.

Accuracy and calibration. Class 1 meters meet IEC 61672 (±0.7 dB, 10 Hz-20 kHz). Cheap meters: ±2-5 dB error, poor low/high frequency response, no calibration. Professional use requires traceable calibration, logging, octave analysis, and durability. Legal/OSHA compliance demands certified equipment.

At 1 kHz: phon = dB SPL exactly (by definition). At other frequencies: they diverge due to ear sensitivity. Example: 60 phon requires 60 dB at 1 kHz, but 70 dB at 100 Hz (+10 dB) and 55 dB at 4 kHz (-5 dB). Phon accounts for equal-loudness contours, dB does not.