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Sound Intensity Frequency Tool

Compute sound intensity I = P / (4π·r²) at any distance from a point source, then apply A-weighting or C-weighting per IEC 61672. Includes ISO 226 threshold-of-hearing reference at the chosen frequency to determine audibility margin.

Input

W
m
Hz
10 Hz100 Hz1 kHz10 kHz20 kHz
Scenarios

Result

Sound intensity (I)
SPL (Z, unweighted)
SPL (A-weighted)
SPL (C-weighted)
Threshold of hearing
Audibility margin (SPLZ − threshold)
Formulas
Intensity: I = P / (4π·r²) (free-field point source)
SPL (Z) = 10·log₁₀(I / 10⁻¹² W/m²)
dBA = SPL + A(f), dBC = SPL + C(f) (per IEC 61672)
Threshold of hearing per ISO 226 (binaural MAF)
A and C weighting curves (IEC 61672)
A-weighting C-weighting

A & C Weighting at Common Frequencies

FrequencyA-weightingC-weightingThreshold (MAF)
20 Hz−50.4 dB−6.2 dB76 dB
31.5 Hz−39.5 dB−3.0 dB65 dB
63 Hz−26.2 dB−0.8 dB50 dB
125 Hz−16.2 dB−0.2 dB35 dB
250 Hz−8.7 dB0 dB19 dB
500 Hz−3.2 dB0 dB9 dB
1 kHz0 dB (ref)0 dB (ref)3.6 dB
2 kHz+1.2 dB−0.2 dB1.4 dB
4 kHz+1.0 dB−0.8 dB−3.9 dB (most sensitive)
8 kHz−1.1 dB−3.0 dB15.3 dB
16 kHz−6.6 dB−8.5 dB13.4 dB
20 kHz−9.3 dB−11.2 dB~40 dB

About Sound Intensity & Frequency Weighting

Sound intensity (W/m²) is the acoustic power flowing through a unit area perpendicular to the wavefront. For a point source radiating into free space, intensity drops with the square of distance: I = P / (4π·r²). This is the inverse-square law in its purest form.

Why frequency weighting?

Human hearing is not equally sensitive to all frequencies. We hear best around 2-5 kHz and progressively worse at the extremes. A 60 dB tone at 100 Hz sounds about as loud as a 35 dB tone at 1 kHz. A-weighting applies a filter that approximates this sensitivity at moderate levels (~40 phon equal-loudness contour). When a measurement is reported as "dBA", it has been filtered this way and roughly corresponds to perceived loudness.

A-weighting (dBA) vs C-weighting (dBC)

A-weighting heavily attenuates low frequencies (−50 dB at 20 Hz) and somewhat attenuates very high frequencies. It's the standard for environmental noise, workplace OSHA exposure, and consumer product noise specs. C-weighting is nearly flat across the audible band (−0.2 dB at 250 Hz to 4 kHz) and only rolls off below 30 Hz and above 6 kHz. It's used for peak and impulse measurements (gunshots, explosions, machinery startup transients) where low-frequency content matters and where A-weighting would discard real energy.

Threshold of hearing (MAF, ISO 226)

The minimum audible field is the quietest tone an average young listener with normal hearing can detect, measured binaurally in a free field facing the source. It varies dramatically with frequency: ~76 dB SPL at 20 Hz, ~3.6 dB SPL at 1 kHz, dipping to ~−4 dB SPL at 4 kHz (most sensitive), and rising sharply above 10 kHz. This tool uses the ISO 226 standard threshold curve and interpolates between standard frequencies.

"Audibility margin"

The audibility margin is how many dB above the threshold of hearing the (A-weighted) SPL sits. Positive values are audible — about +20 dB is "clearly audible", +60 dB is "loud", +100 dB approaches pain. Negative values are inaudible to typical listeners but can still cause harm to hearing in some cases (very high SPL at non-audible frequencies still pumps energy into the inner ear).

Frequently Asked Questions

Why does dBA show ear-friendly numbers but dBC sometimes shows much higher?
Because A-weighting throws away low-frequency energy that the ear is largely insensitive to, while C-weighting keeps it. A bass-heavy concert at 90 dBC might be only 75 dBA — same physical energy, but dBA "predicts" loudness perception while dBC reports the full audio energy. OSHA noise limits use dBA precisely because hearing damage correlates better with A-weighted exposure than raw SPL.
What's the difference between Z, A, and C weighting?
Z (zero / linear / Lin / Flat) is no weighting at all — the raw SPL across the bandwidth. A mimics the 40-phon equal-loudness contour (suited to moderate noise levels). C is nearly flat in the mid-band, used for peaks and high-level measurements. There's also B-weighting (between A and C, 70 phon) but it's deprecated. Modern usage: A for environmental/occupational noise, C for peaks, Z when you want raw physics.
Does the inverse-square law account for room reflections?
No — I = P/(4π·r²) assumes a point source in unbounded free space (anechoic outdoors). In a real room, reflections add energy, raising measured SPL above the free-field prediction. The room's reverberant field eventually dominates at distances beyond the critical distance, where direct and reverberant levels are equal. For typical living rooms this is 1-3 m. Use this tool's free-field result as a baseline; add 3-10 dB for normal-room behavior.
Why is the threshold of hearing negative dB SPL above 1 kHz?
Because the 0 dB SPL reference (20 µPa) was anchored to the threshold at 1 kHz, but the ear is even more sensitive between 2-5 kHz. At 4 kHz, the threshold drops to about −4 dB SPL. People with very acute hearing can detect tones at −5 to −10 dB SPL in this range. Anechoic chambers can even measure ambient noise below 0 dB SPL — silence quieter than the threshold of human hearing.
Does A-weighting account for hearing damage risk?
Approximately, yes. OSHA's permissible exposure limit is 90 dBA for 8 hours (or 85 dBA in tougher standards). Each +5 dB halves the allowable time — so 95 dBA → 4 hr, 100 dBA → 2 hr, etc. But A-weighting underestimates damage from impulses (gunshots) and from sustained high-level low-frequency sources, which is why peak/C-weighted limits also apply.
What's the relationship between sound intensity and sound pressure level?
For a plane progressive wave: I = p²/(ρc) where p is RMS pressure, ρ is air density (~1.2 kg/m³), and c is speed of sound (~343 m/s). So ρc ≈ 411 N·s/m³ (acoustic impedance of air). At 1 Pa RMS pressure: I = 1/411 ≈ 2.4 mW/m² ≈ 94 dB SPL. The dB scales are designed so that SPL and intensity level numerically coincide in air at standard conditions — convenient since it lets us measure pressure (microphones) and report intensity-equivalent dB.