What Near Field and Far Field Mean for a Measurement

Why this matters

A tech puts a meter about six inches off a compressor cabinet, reads a number, and the office puts it in a report next to a manufacturer's published figure. The two disagree by a wide margin and an argument starts about whose data is wrong. Neither is. The reading was taken in a region where no distance law applies and where pressure is not a reliable stand-in for radiated energy, so it was never the same kind of quantity as the published figure. Worse, in the room where it was taken there was no position at which a valid comparison measurement could have been made at all. Knowing that before the visit takes about two minutes of arithmetic and saves the whole argument.

The call, and the reading that was taken

Complaint: a steady low hum in an adjacent office, dominated by a 120 Hz tone. Source suspected to be a packaged compressor in the plant room next door. The cabinet is 1.2 m tall and 0.9 m wide, sitting on a hard floor away from the walls. The plant room is 6 m by 5 m by 3 m, bare block and concrete.

The tech held the meter about 0.15 m off the cabinet face, read an A-weighted overall level, wrote it down, and left. That number then travelled into a report as if it described the machine.

Two boundaries, and what each one is

There are two independent boundaries on where a microphone may usefully stand, and they come from opposite directions.

The source-side boundary: the near field. You must be far enough away that the source behaves as one radiating thing and that pressure tracks radiated energy. Two criteria set it and you take whichever is larger.

• The hydrodynamic criterion. Very close to a vibrating surface, air is being sloshed back and forth locally rather than radiated away. Pressure and particle velocity are out of phase there, so a pressure reading includes energy that never leaves. Clear this by standing at least about one wavelength of the lowest frequency of interest away.
• The geometric criterion. Close to an extended source, different parts of the source sit at meaningfully different distances from the microphone, so no single distance law describes the sum. Clear this by standing at least about twice the largest source dimension away.

The room-side boundary: the critical distance. You must be close enough that the direct field still dominates the reverberant field. Past the critical distance you are measuring the room. The arithmetic for it belongs to the sibling card on why the same machine reads differently in two rooms, and it is used here as that card states it: critical distance in metres is 0.141 times the square root of (Q times R).

A valid far-field, direct-field measurement position exists only in the window between those two boundaries. Sometimes there is no window.

Running the numbers on where the tech stood

Source-side boundary. Largest cabinet dimension 1.2 m, so the geometric criterion gives 2 x 1.2 = 2.4 m. Lowest frequency of interest 120 Hz; at 343 m/s in air at about 20 C, that wavelength is 2.9 m, so the hydrodynamic criterion gives 2.9 m. Take the larger: 2.9 m.

Where the tech actually stood. 0.15 m. That is 0.13 of the largest source dimension and about 0.05 of a wavelength at the frequency the complaint is about. Not marginally inside the near field. Deep inside both criteria.

Room-side boundary. The plant room's interior surface area is 126 square metres and the overall room constant for these bare surfaces is 6.63 square metres, taken from the sibling card's worked room rather than re-derived. With the compressor on the floor away from walls, Q = 2, so the critical distance is 0.141 times the square root of (2 x 6.63) = 0.51 m.

One qualifier attached rather than left downstream: 6.63 is an overall figure, and bare masonry absorbs less at 125 Hz than its overall average, so the room constant in the band that actually matters here is lower and the critical distance is shorter still. Every correction available runs the same way.

The collision

The source-side boundary says stand no closer than 2.9 m. The room-side boundary says stand no farther than 0.51 m. The far field of the source begins about 5.7 times farther out than the point at which the room takes over the reading.

There is no valid measurement position in that room. Not a poor one, not a compromised one: none. Every position is either inside the source's near field, where distance laws do not apply and pressure over-reads what is radiating, or outside the critical distance, where you are characterising the plant room. The 0.15 m reading fell in the first category and the 3 m reading the tech might have taken instead would have fallen in the second.

What it would take to open a window. For the critical distance to reach 2.9 m in this room, the room constant would have to be about 211 square metres, which against 126 square metres of surface requires an average absorption coefficient near 0.63 on every interior surface including the floor, at the frequency of interest. That is not a plant room. The correct conclusion is not to treat the room; it is that this measurement cannot be made here.

Reconciling this with an extended source

An obvious objection: the sibling inverse-square card measures an array 20 m long from 2.0 m away, which is far inside that array's geometric near field, and treats the result as valid. That is not a contradiction, and the resolution is worth stating because it is the practical rule.

The geometric criterion applies to whatever you intend to characterise as a compact source. If you cannot clear it, the answer is not to take a bad point-source measurement. It is to switch to the model that matches the geometry: a line source measured within its own extent behaves as a line and falls off at 3 dB per doubling rather than 6, and that model is valid exactly where the point model is not. The failure mode is not standing close. It is standing close and applying the compact-source rules anyway.

What the six-inch reading is actually worth

It is not worthless. It is worth exactly one thing, and it is worth it only if the position is recorded.

It is a repeatable relative indicator. Marked position, same distance, same orientation, same operating state, same weighting and time basis: read it monthly and a rise means something changed in the machine. The room's contribution and the near-field behaviour are both present in every reading and both cancel out of the comparison.

It is not extrapolatable. No distance law applies, so it cannot be moved to the property line or to the office next door.

It is not comparable to a published figure, because the published figure was determined under a test method with its own defined surface and environment.

It cannot be converted to sound power, because the conversion assumes free-field far-field conditions this position does not meet.

It is not evidence about a limit, because an ordinance or a specification names its own measurement position and this is not it.

What they did instead

Three routes were open and the shop took the third.

Determine sound power by a method that does not need a free field. Sound power can be determined in a reverberant space or in situ by methods written for that purpose, each with its own defined procedure, environment and grade of accuracy. Those methods bind you only through the specification or purchase document that names them, in the edition it names, and they are the right answer when a machine has to be compared against a published rating.

Move the machine, or measure a like machine outdoors. Rarely practical and worth naming anyway, because it is sometimes the cheapest option on a new-equipment selection.

Measure the position the complaint is about. The office next door is where the problem is, where any criterion applies, and where a before-and-after at one fixed position will honestly show whether a treatment worked. The plant room reading was never going to answer the tenant's question even if it had been valid.

The part that travels

Both boundaries are computed from things you know before you leave the shop: the source's largest dimension, the lowest frequency of interest, the room's dimensions and a rough read on its surfaces. That makes "is a valid measurement possible at this site" a desk decision rather than a field discovery, and it is the cheapest two minutes in this whole subject. A tech dispatched with the answer already known either brings back data or brings back the right question. A tech dispatched without it brings back a number that will be argued over for a month.

Standing close to a running machine to take any of these readings carries its own hazards, and they are not the article's topic, which is exactly why they need naming. 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 reads. Use a stand rather than a handheld meter at close range, positioned outside the plane of any rotating component with guards in place per 29 CFR 1910.212(a)(1), and never reach past a guard. Do not open a compressor cabinet to get a microphone inside it: that is mechanical isolation and stored-energy work under 29 CFR 1910.147, including bleeding receiver pressure down through the drain and confirming zero at the gauge before a panel comes off, and any work at the starter is electrical, which 1910.147 excludes by its own carve-out and 29 CFR 1910.333(b)(2) covers instead.

References

• 29 CFR 1910.212(a)(1) for machine guarding around a microphone position, and 29 CFR 1910.95 for occupational noise exposure in the space
• 29 CFR 1910.147 for mechanical isolation and stored energy, and 29 CFR 1910.333(b)(2) for electrical work, which 1910.147 expressly excludes
• Sound power determination methods appropriate to a reverberant or in-situ environment, in the edition your specification or purchase document names
• See related: Why the Same Machine Reads Differently in Two Rooms; What the Inverse Square Law Covers and Where It Stops