Why the Same Machine Reads Differently in Two Rooms

Why this matters

The same air compressor gets measured at 2 m in the old plant room and reads 88.1. It gets relocated, measured at 2 m again in the new shop, and reads 77.8. Somebody will say the unit got quieter, somebody else will say one of the readings is wrong, and both will be mistaken. The machine did not change. The pressure at a point is a sum of two contributions, only one of which belongs to the source, and the second one is a property of the room's total absorption. Until a shop can separate those two terms, it cannot say what a level means, cannot predict what a treatment will buy, and will keep paying for absorption in rooms where absorption has nothing left to remove.

Two terms, and only one belongs to the machine

At any point in an enclosed space, the sound pressure level is made of:

• The direct field, energy arriving straight from the source without reflecting. It depends on the source's power, the distance, and which way the source radiates. It falls with distance.
• The reverberant field, energy that has bounced off the room surfaces at least once and is now filling the volume. It depends on the source's power and the room's total absorption. In a reasonably diffuse room it is very nearly the same everywhere and does not fall with distance.

For a source in a room, with steady-state operation, the source power held constant, the source small compared with the measuring distance, and a reasonably diffuse reverberant field:

Lp = Lw + 10 log( Q / (4 pi r squared) + 4 / R )

with r in metres and R in square metres. Q is the directivity factor: 2 for a source sitting on a large hard floor away from walls, 4 at a floor-wall junction, 8 in a corner. R is the room constant.

The room constant, and what it is derived under

R = S x alpha, divided by (1 minus alpha), where S is the total interior surface area in square metres and alpha is the area-weighted average absorption coefficient of those surfaces.

Two conditions travel with that expression and both matter in the field. It assumes the absorption is distributed reasonably evenly, so a room with a heavily treated ceiling and bare everything else departs from it. And alpha is frequency-dependent: a fibrous absorber that reads high at 1 kHz can read very low at 125 Hz, so R computed from a single average number is an overall approximation and a per-band calculation is what a treatment decision needs.

The crossover: where the room takes over

The two terms are equal at a distance called the critical distance, and past it the room's contribution dominates.

Critical distance, in metres: 0.141 times the square root of (Q times R).

Inside it, moving the microphone changes the reading. Outside it, moving the microphone barely changes anything, because you are measuring the room, not the machine. That single fact explains most arguments about where the tech "should have stood".

Worked example: one machine, two rooms

A packaged compressor with a sound power level of 90 dB re 1 picowatt, A-weighted, overall. Sound power is a property of the source, so it is the same figure in both rooms; that claim is the sibling power-versus-pressure card's, and it is used here rather than re-derived.

Measurement basis in both rooms: A-weighted, overall, equivalent-continuous sound pressure level re 20 micropascals, microphone on a stand 2.0 m from the machine at 1.5 m above the floor. Machine sitting on a hard floor away from walls, so Q = 2 in both.

Room A, the old plant room. 6 m by 5 m by 3 m. Interior surface area S = 126 square metres. Bare block and concrete, average absorption coefficient 0.05.

• R = 126 x 0.05 / 0.95 = 6.63 square metres
• Direct term at 2.0 m: 2 / (4 pi x 4) = 0.0398
• Reverberant term: 4 / 6.63 = 0.6032
• Sum = 0.643, and 10 log 0.643 = -1.9
• Lp = 90 - 1.9 = 88.1 dB

The reverberant term is 93.8% of the total. This reading is almost entirely the room.

Room B, the new shop. 20 m by 12 m by 5 m. Interior surface area S = 800 square metres. Absorptive deck and some wall treatment, average absorption coefficient 0.20.

• R = 800 x 0.20 / 0.80 = 200 square metres
• Direct term at 2.0 m: unchanged at 0.0398, because the distance, the directivity and the source are all unchanged
• Reverberant term: 4 / 200 = 0.0200
• Sum = 0.0598, and 10 log 0.0598 = -12.2
• Lp = 90 - 12.2 = 77.8 dB

The direct term is now 66.6% of the total.

The result. The identical machine, at the identical distance, on the identical basis, reads 88.1 dB in one room and 77.8 dB in the other. The gap is 10.3 dB, and neither figure is an error. Report either one without its room and you have published a number that cannot be reproduced anywhere else on earth.

Critical distance, printed for each, because it is the qualifier that tells you what the reading is. Room A: 0.141 times the square root of (2 x 6.63) = 0.51 m. The microphone at 2.0 m sits nearly four times past it, so Room A's reading is a reverberant-field reading and moving the stand a metre would change almost nothing. Room B: 0.141 times the square root of (2 x 200) = 2.82 m. The microphone at 2.0 m sits inside it, so Room B's reading is direct-dominated and moving the stand a metre would change it noticeably. Two readings taken with identical technique are not even the same kind of measurement.

What absorption can and cannot buy

Absorption acts on the reverberant term only. It cannot touch the direct term, so no amount of it can take a point below the level it would have in a free field at that distance.

Room A, doubling the absorption. Raise alpha from 0.05 to 0.10. R goes to 14.0 square metres, so the reverberant term falls from 0.6032 to 0.2857. The reverberant term alone has dropped 3.2 dB. The total drops from 0.643 to 0.3255, which is 2.95 dB, because the direct term did not move at all. That gap between 3.2 and 2.95 is small here and it grows: every decibel you take out of the reverberant field makes the direct term a bigger share of what is left, so each successive doubling of absorption returns less than the one before.

Room B, the floor. Set the reverberant term to zero, which is the best any absorption purchase could ever do. Lp = 90 + 10 log(0.0398) = 76.0 dB. Room B already reads 77.8 dB, so the entire remaining budget of absorption at that position is 1.8 dB, and most of it is unreachable. A shop quoting an absorption package for Room B on the strength of what it did in Room A will deliver something the customer cannot hear.

Sibling-rule check on this scenario, printed. Sound power is held at 90 dB re 1 picowatt in both rooms, which is what the power-versus-pressure card requires and what makes the comparison legal. All levels are A-weighted, overall, equivalent-continuous, re 20 micropascals, at 2.0 m and 1.5 m height, in both rooms, so no basis switches between the two halves. Distances are in metres throughout, areas in square metres throughout. Q = 2 is applied identically in both rooms and is the on-floor value, not the corner value. No number appears in the example that the general section did not state.

Reverberation time is the field proxy for absorption

You will rarely be handed a room's absorption coefficient. Reverberation time is measurable and is set by the same quantity. Sabine's relationship, valid for a reasonably diffuse field at low to moderate average absorption, roughly alpha below about 0.2:

T60 = 0.161 x V / A, with V the volume in cubic metres and A the total absorption in square metres of the surfaces, which is S times alpha.

• Room A: V = 90 cubic metres, A = 126 x 0.05 = 6.3. T60 = 2.30 s.
• Room B: V = 1,200 cubic metres, A = 800 x 0.20 = 160. T60 = 1.21 s.

Room B sits right at the edge of Sabine's validity, so treat its figure as indicative; above about 0.2 average absorption the Eyring form is the appropriate one and the reference for it is a room-acoustics text, not this card. What the two numbers are genuinely good for is the field judgement: clap once in each room and Room A rings for about twice as long. That is the direct sensory read on whether you are standing in a room that will dominate your measurement.

Checking which term you are in, before you trust a reading

Walk the microphone. Take a reading, move the stand to double the distance, take another. A drop approaching 6 dB per doubling says you are direct-dominated and inside the critical distance. A drop of a decibel or less says you are in the reverberant field and the number belongs to the room. The conditions under which the 6 dB figure holds, and the ways it fails for reasons that have nothing to do with the room, are the inverse-square card's subject.

Compute the critical distance before you go. If you know the room dimensions and can estimate the surfaces, you know before you arrive whether a direct-field measurement is even possible at a workable distance.

Never compare a level across rooms. Compare sound power levels across rooms, or compare a before and after at one fixed position in one room, where the room's contribution is identical in both readings and cancels out of the difference.

Room A reads 88.1 dBA with the machine running. A short measurement stint there is a small fraction of the daily allowable dose under 29 CFR 1910.95 Table G-16, but a person who works that room all shift is a different question entirely, and 1910.95(d)(1) requires monitoring wherever information indicates an employee's exposure may equal or exceed an 8-hour time-weighted average of 85 dBA. Wear hearing protection in any space where you must raise your voice to be heard at arm's length, and note it changes what you hear, not what the microphone on the stand reads. Place the stand outside the plane of any rotating component with guards in place per 29 CFR 1910.212(a)(1), and never reach past a guard to position a microphone.

References

• 29 CFR 1910.95, Occupational noise exposure, including Table G-16 permissible exposures and the monitoring trigger at (d)(1)
• 29 CFR 1910.212(a)(1) for machine guarding around a microphone position
• Absorption coefficient data from the product's own test report, per band, with the test method and mounting it was measured under
• See related: Why Sound Power and Sound Pressure Are Not the Same Number; What the Inverse Square Law Covers and Where It Stops