Sound Masking System Design: Spectrum, Level, and Coverage Calculation

Sound masking is often specified as a single number — "install a masking system to 45 dBA" — but this misses the engineering. An incorrectly shaped masking spectrum provides poor intelligibility reduction even at the right level, and poor speaker placement creates hot spots and dead zones that make the system audible as a distinct sound rather than transparent background noise. This article designs a masking system for a real 500 m² open office from first principles, with every number calculated explicitly.

The Space

Floor plan: 25 m × 20 m open office, 2.7 m floor-to-ceiling height (suspended acoustic ceiling) Occupancy: 60 workstations, 60% occupancy during peak hours Existing ceiling: 600 × 600 mm mineral fibre tile, NRC 0.75 Problem: Speech is intelligible at 8 m distance. Privacy Index is below 60%. Staff complaints about distraction.

Step 1 — Baseline Acoustic Measurements

Before designing the masking system, we need to know the existing acoustic environment. Field measurements taken at five representative positions during unoccupied working hours (HVAC running, no occupants):

Existing background noise levels (unoccupied, HVAC only):

This is a very quiet office — HVAC noise sits below NR 30. Speech is almost entirely unmasked. We can expect high intelligibility at long distances.

Occupied speech level at workstation (talker 1 m from mouth, typical conversational voice):

Step 2 — Speech Propagation to Receiver

In an open plan office with a good acoustic ceiling, speech level attenuates with distance following a power law influenced by the ceiling's absorption. Using the ISO 3382-3:2012 method, the spatial decay rate D_2,S is measured or estimated.

For this ceiling (NRC 0.75, room geometry), a typical D_2,S value is approximately 4.5 dB per distance doubling.

Speech level at distance r from talker:

L(r) = L(1m) - D_2,S × log₂(r)

For r = 8 m (distance we're targeting for privacy):

log₂(8) = 3.0

Attenuation = 4.5 × 3.0 = 13.5 dB

Speech level at 8 m receiver position (per octave band):

A-weighted speech at 8 m ≈ 52 dBA (applying standard A-weighting corrections).

Step 3 — Calculate the Articulation Index (Before Masking)

The Articulation Index uses the signal-to-noise ratio (SNR) in each band, weighted by the importance of that band to speech intelligibility. Using the simplified AI method from ANSI S3.5:

AI band weight factors:

SNR per band = L_speech(r) − L_noise

AI = Σ(W_i × SNR_norm) = 0 + 0.010 + 0.130 + 0.330 + 0.300 + 0.119 = 0.889

An AI of 0.89 corresponds to very high intelligibility — almost every word understood at 8 m. Privacy Index = 1 − AI = 0.11, or 11%. This confirms the problem.

Target: AI < 0.15 (Privacy Index > 85%) at 8 m distance.

Step 4 — Design the Masking Spectrum

The masking noise spectrum must:

1. Sit above the existing background noise (to be effective)
2. Match the shape of speech to maximise masking per dB added
3. Avoid harsh, audible tonality that creates occupant complaints

This curve rolls off at high frequencies to match the characteristic roll-off of speech energy and avoid the spectrum sounding "bright" or hissing.

Verify the masking spectrum exceeds existing background noise at every band:

All bands confirm. A-weighted level of masking spectrum: applying A-weighting corrections (125 Hz: −16.1 dB, 250 Hz: −8.6 dB, 500 Hz: −3.2 dB, 1 kHz: 0 dB, 2 kHz: +1.2 dB, 4 kHz: +1.0 dB):

Energy sum: 10 × log₁₀(10^3.49 + 10^4.14 + 10^4.48 + 10^4.60 + 10^4.52 + 10^4.10)

= 10 × log₁₀(3090 + 13800 + 30200 + 39800 + 33100 + 12600)

= 10 × log₁₀(132590) = 51.2 dBA

This is within the recommended 48–52 dBA range for open offices. It will be perceptible but should not be annoying if the spectrum is correctly shaped.

Step 5 — Calculate the Articulation Index (After Masking)

With the masking system active, the noise floor at the receiver is now the masking spectrum (replacing existing background noise which is lower):

AI (after masking) = 0 + 0.0052 + 0.0845 + 0.2035 + 0.1450 + 0.0542 = 0.492

Hmm — still too high. AI = 0.49 gives Privacy Index = 51%. We need the masking level to be higher, or the receiver distance to be shorter, or both.

Adjust masking level: raise all bands by 4 dB:

AI (revised) = 0 + 0.004 + 0.067 + 0.160 + 0.105 + 0.037 = 0.373

Still above target. This reveals an important truth: masking alone cannot achieve AI < 0.15 in a space with this level of speech intelligibility at 8 m. Sound masking works best when combined with spatial planning (workstation spacing) and acoustic absorption to increase D_2,S.

If the D_2,S rate could be improved from 4.5 to 6.0 dB/doubling (achievable by adding absorptive screens at workstation height), the speech level at 8 m drops by an additional:

(6.0 − 4.5) × log₂(8) = 1.5 × 3.0 = 4.5 dB reduction

With speech reduced by 4.5 dB and revised masking at +4 dB:

AI (combined strategy) ≈ 0 + 0.003 + 0.048 + 0.110 + 0.060 + 0.017 = 0.238

Closer. With the full treatment (masking + screens + ceiling optimisation), AI < 0.15 is achievable. This shows that masking system design must be integrated with the overall acoustic strategy.

Step 6 — Speaker Layout and Coverage Calculation

Ceiling height: 2.7 m Speaker type: downward-facing directional emitter, cone angle ±45° (90° total) Coverage radius per speaker at ceiling: r = H × tan(45°) = 2.7 × 1.0 = 2.7 m

For ±2 dB uniformity, speakers must overlap by at least 30%. Effective coverage spacing:

Spacing = 2 × r × 0.85 (15% overlap each side) = 2 × 2.7 × 0.85 = 4.6 m

Grid layout for 25 m × 20 m floor:

• Along 25 m axis: 25 / 4.6 = 5.4 → 6 columns at 25/6 = 4.17 m spacing
• Along 20 m axis: 20 / 4.6 = 4.3 → 5 rows at 20/5 = 4.0 m spacing

Zone boundaries: Split the floor into 4 zones for independent level control (zones allow tuning around glass walls, entrance lobbies, and high-traffic areas that receive more masking).

Step 7 — System Power Budget

Each speaker delivers sound pressure level determined by its sensitivity and drive level. For a typical ceiling masking speaker:

• Rated sensitivity: 82 dB SPL at 1 m, 1 W
• Target level at floor: 51 dBA (revised masking level at 500 Hz: 52 dB)
• Distance from speaker to ear: 2.7 m (direct path, ceiling to seated height 1.2 m = 1.5 m ear height, so d = 2.7 − 1.2 = 1.5 m effective)

52 = 82 + 10 × log₁₀(W) − 20 × log₁₀(1.5)

52 = 82 + 10 × log₁₀(W) − 3.5

10 × log₁₀(W) = 52 − 82 + 3.5 = −26.5 dB

W = 10^(−2.65) = 0.0022 W per speaker (2.2 mW)

For 30 speakers: total amplifier demand = 30 × 0.0022 = 0.066 W into speakers. Amplifier overhead ×10: target amplifier capacity ~1 W per channel, with 30 channels. In practice, a 4-channel amplifier driving 8-speaker zones is common for spaces of this size.

Step 8 — Commissioning Acceptance Criteria

Set the commissioning pass/fail criteria before installation. Measure at 20 representative points with the system active:

Summary of Results

The key lesson from this calculation is that sound masking alone in a poorly performing space achieves limited privacy improvement. The masking system reduces AI from 0.89 to approximately 0.37 on its own. Achieving the target AI < 0.15 requires integrating masking with acoustic screens and ceiling treatment. Specify all three together; budget for all three together.

Use AcousPlan's speech privacy calculator to model your specific open office configuration and optimise the combined treatment strategy before committing to a masking system specification.