A 40 Hz drone that passes the dB(A) permit limit
You are engaged by a residents' group in a mid-rise apartment building. Since the neighbouring cold-store upgraded its refrigeration plant eighteen months ago, occupants of two flats report a constant 'pressure in the ears' and four to five awakenings a night. The operator's consultant has reported 38 dB LAeq at the facade at night against a permit limit of 45 dB(A), and declared compliance. You attend with a Class 1 analyser giving one-third-octave bands from 20 Hz to 10 kHz, a pistonphone, and a tripod. With the plant running, the one-third-octave spectrum at the complainant's window is dominated by a single band at 40 Hz, 68 dB; every other band is below 50 dB. With the plant off, the 40 Hz band is 52 dB and the overall level is 31 dB(A). The plant-on overall level is 39 dB(A). The resident has kept a diary of 40 disturbed nights and has sent it to the local authority. Your client asks whether the permit limit is the whole story.
1. The A-weighted total is well below the permit limit. Explain, with numbers, why that does not settle the question.
Read the worked answer
A-weighting at 40 Hz is about -34.6 dB. A 68 dB component in that band therefore contributes only about 33.4 dB(A) to the total; the rest of the 39 dB(A) comes from bands above roughly 100 Hz. So the metric that the permit is written in is precisely the metric that discards the energy the residents are reacting to.
The A-weighting curve was derived from equal-loudness contours at low sound levels. It is a reasonable predictor of annoyance for broadband mid-frequency noise, and a poor one for a dominant low-frequency tone, where the reported effects are pressure sensations, rumble and sleep disturbance rather than loudness. C-weighting at 40 Hz is only about -2 dB and dB(Z) is flat, so either would show the plant dominating the spectrum.
The defensible position is not that the permit is wrong, but that '38 dB(A), compliant' answers only the A-weighted legal question. The report should have disclosed the one-third-octave spectrum, and the assessment should have applied a criterion with a low-frequency penalty or a separate low-frequency limit at the facade. Compliance with a permit condition and absence of a nuisance are two different findings, and a report that presents only the first as though it were the second is incomplete rather than false.
2. The plant-off level in the 40 Hz band is 52 dB. What is the background-corrected level, and what instrument checks would you make before reporting it?
Read the worked answer
Corrected level = 10 log(10^(68/10) - 10^(52/10)) = 10 log(6.31x10^6 - 1.585x10^5) = 10 log(6.15x10^6) = 67.9 dB. The correction is 0.1 dB, i.e. negligible, because the plant-on level is 16 dB above background. As a rule: difference under 3 dB means report only an upper bound, never a corrected number; 3 to 10 dB means correct and state that the result carries uncertainty of up to about 3 dB; over 10 dB means the correction can be ignored.
Before reporting it, check the instrument chain at the frequency that matters. The pistonphone verifies the system at 1 kHz only and says nothing about low-frequency response. Confirm the microphone and preamplifier noise floor: self-noise in the 20-50 Hz region can be high enough to contaminate a quiet 52 dB plant-off measurement. Confirm no A-weighting or rumble filter is engaged in the analyser path, and that the displayed band values are dB(Z). Check the windscreen, the measurement height (1.2-1.5 m, away from a reflective balcony soffit), and whether the 40 Hz energy could be mains-related or from the complainant's own building services. Finally, note that one position at one window is a point measurement, not a facade assessment.
3. What do you recommend to the local authority that is holding the permit?
Read the worked answer
I would not recommend 'compliance, close the file', and I would not ask the authority to accept the 38 dB(A) figure as a complete assessment. The recommendations would be:
- Require the operator to supply octave-band sound power data for the refrigeration plant, including night-time control settings, rather than only an A-weighted result.
- Require the noise condition to be restated so it can be tested against this spectrum: a dB(A) limit plus a low-frequency limit in dB(Z) or dB(C) at the affected facade, or a rating that carries a low-frequency adjustment.
- Ask for a joint measurement with agreed positions, instrumentation and plant operating states, so the dispute is not resolved by competing single-point surveys.
- Note that 15-25 dB reduction at 40 Hz is usually achievable on refrigeration plant through enclosure, revised fan speed and isolation, so mitigation is not speculative.
I would also state the limits of my own evidence: one window position, a short survey, and no diagnostic access to the plant. The honest framing is that the A-weighted result is probably correct and the assessment is still inadequate, and the authority may need to review the form of its own condition rather than just this operator's compliance.