Engineer Noise and Vibration cheat sheet

Sound pressure level: Lp = 20 log10(p/p0), p0 = 20 µPa; sound power level: Lw = 10 log10(W/W0), W0 = 1 pW; intensity level: LI = 10 log10(I/I0), I0 = 1 pW/m².

Decibel addition: L_total = 10 log10(Σ 10^(Li/10)); adding two equal levels raises the sum by 3 dB, and a source 10 dB lower adds 0.4 dB.

For a point source in a free field, SPL falls 6 dB per doubling of distance; for a line source (road traffic at moderate distance) the fall is 3 dB per doubling.

A-weighting approximates the 40-phon equal-loudness contour; B- and C-weighting correspond to 70 and 100 phon. C-weighting is used for peak and high-level assessments.

Frequency bands: octave band edges follow fc = 1000·2^n with f_upper/f_lower = 2; one-third-octave bands use ratio 2^(1/3) ≈ 1.26, and the 1 kHz band spans 891–1122 Hz.

Room acoustics: reverberation time Sabine formula RT60 = 0.161 V/A (metric, V in m³, A in m² sabins); absorption coefficient α = absorbed/incident energy.

Simple harmonic motion: x = X sin(ωt), velocity amplitude v = ωX, acceleration amplitude a = ω²X; at 1 kHz, a = 1 m/s² corresponds to v ≈ 0.159 mm/s and x ≈ 25 nm.

Vibration descriptors: RMS, peak, peak-to-peak, and crest factor = peak/RMS; for a sinusoid RMS = peak/√2 and crest factor = 1.414.

Frequency weighting for hand-arm vibration: Wh weights mid frequencies most heavily; for whole-body vibration Wk is the primary weighting, with Wd, Wf, Wc used for specific axes and conditions.

Sound level meters are graded by IEC 61672 as Class 1 or Class 2; Class 1 has tighter tolerances (±0.7 dB at reference conditions versus ±1.0 dB for Class 2).

Before and after each measurement set, calibrate with a pistonphone or sound calibrator; a drift greater than 0.5 dB invalidates the measurement and requires investigation.

Fast (F) time weighting is 125 ms, Slow (S) is 1000 ms, and Impulse (I) is 35 ms rise with a slower decay; LAeq is an energy average and is independent of time weighting.

LAeq,T = 10 log10[(1/T)∫(pA²/p0²)dt]; for discrete samples, LAeq = 10 log10[(1/N)Σ10^(Li/10)].

LAE (SEL) = LAeq + 10 log10(T/T0) with T0 = 1 s; Lden = 10 log10[(1/24)(12·10^(Lday/10) + 4·10^((Levening+5)/10) + 8·10^((Lnight+10)/10))].

A single-number rating from octave-band data: for airborne sound insulation, Rw is derived from the reference curve; for impact sound, Ln,w uses a shifted reference curve.

FFT analyzer: frequency resolution Δf = fs/N and record length T = 1/Δf; a Hanning window reduces spectral leakage but broadens peaks by about 1.5 bins.

Nyquist criterion: sampling frequency must exceed twice the highest frequency of interest; anti-alias filtering is required before sampling.

Microphone directivity and wind: use a windscreen outdoors, and note that wind-induced noise on a 200 mm windscreen can bias low-level measurements; a 90 mm windscreen is standard for environmental work.

OSHA PEL: 90 dBA as an 8-hour TWA with a 5 dB exchange rate; the action level is 85 dBA TWA, triggering audiometric testing and training.

OSHA hearing conservation program triggers at 85 dBA TWA; engineering and administrative controls are required before relying on hearing protectors at or above 90 dBA.

NIOSH REL: 85 dBA for 8 hours with a 3 dB exchange rate; permissible time T = 8/2^((L−85)/3) hours.

Dose conversion: D = 100·(C1/T1 + C2/T2 + …); a dose of 100% at the OSHA criterion equals 90 dBA TWA.

Standard threshold shift (OSHA): average change of 10 dB or more at 2000, 3000, and 4000 Hz in either ear; recordable if the shift averages 10 dB and the hearing level is 25 dB or more.

Hearing protector attenuation: NRR (EPA) is applied as estimated exposure = dBA − (NRR − 7); derating factors of 25% (OSHA), 50% (NIOSH), or 75% may be applied.

Impulse noise: OSHA sets a 140 dB peak limit; NIOSH recommends 140 dBC peak for impulse and 85 dBA for continuous exposure.

Audiometric testing: baseline within 6 months of first exposure, annual thereafter; test in a booth meeting ANSI S3.1 background noise limits.

Propagation outdoors: geometric spreading, atmospheric absorption (increases with frequency and humidity), ground effect, and barrier insertion loss; a barrier must break line of sight to be effective.

Barrier insertion loss is limited to about 20 dB in practice; the Maekawa method uses Fresnel number N = 2δ/λ, with IL ≈ 10 log10(3 + 20N).

Atmospheric absorption at 4 kHz is roughly 10–30 dB/km depending on temperature and humidity; at 125 Hz it is under 1 dB/km.

Lden uses day 07:00–19:00, evening 19:00–23:00 (+5 dB), and night 23:00–07:00 (+10 dB); Ldn uses day/night with a +10 dB night penalty.

Lnight is the A-weighted equivalent level over the night period and is the EU indicator for sleep disturbance assessment under the Environmental Noise Directive.

Road traffic: pass-by level depends on speed, pavement type, and gradient; a 3 dB change is generally the threshold of noticeable change in steady traffic noise.

Aircraft noise: SEL and LAmax are used for single events; cumulative metrics include Lden and the number-above-threshold approach (NAT).

Meteorological effects: temperature inversions and downwind propagation can increase levels by 10 dB or more at distances over 500 m compared with neutral conditions.

Control hierarchy: reduce at source, then path, then receiver; source control is generally the most cost-effective and durable.

Mass law for a single-leaf partition: TL ≈ 20 log10(m·f) − 47 dB (m in kg/m², f in Hz); doubling mass or frequency adds about 6 dB.

Coincidence dip occurs when the trace wavelength in the panel matches the airborne wavelength; it lowers TL around the critical frequency fc = c²/(1.8·cL·h).

A double-leaf partition outperforms a single leaf of equal mass if the cavity is at least 50–100 mm and filled with absorptive material; the mass-air-mass resonance must be placed below the frequency range of concern.

Silencer types: dissipative (absorptive) silencers attenuate mid-to-high frequencies; reactive silencers attenuate low frequencies via expansion chambers and resonators.

Vibration isolation: transmissibility T = 1/|1 − (f/fn)²| for an undamped system; isolation begins above f/fn = √2 and improves 12 dB per octave beyond it.

Static deflection δ (mm) relates to natural frequency: fn ≈ 15.76/√δ Hz; a 25 mm deflection gives about 3.2 Hz.

Structure-borne transmission is controlled with resilient mounts, inertia blocks, and flexible couplings; rigid connections short-circuit isolation and must be avoided.

Hearing damage risk increases with both level and duration; the equal-energy hypothesis underlies the 3 dB exchange rate used by NIOSH and ISO 1999.

Presbycusis: hearing threshold rises with age, roughly 1 dB per year above 1 kHz after age 40 for men, less for women; ISO 7029 provides age-related distributions.

Noise-induced hearing loss typically shows a notch at 3000–6000 Hz, most often at 4000 Hz, with recovery at 8000 Hz.

Annoyance: ISO/TS 15666 specifies the 11-point numerical scale and the 5-point verbal scale for social surveys; %HA is often modeled from Lden.

Sleep disturbance: Lnight is the primary EU indicator; intermittent events and LAmax inside bedrooms are relevant to awakening.

Vibration: ISO 2631-1 uses frequency-weighted acceleration and the daily vibration dose value VDV = [∫a_w⁴(t)dt]^(1/4); the eVDV estimate is 1.4·a_w·T^(1/4).

Hand-arm vibration: ISO 5349-1 uses A(8) = a_hv·√(T/T0) with T0 = 8 h; the EU action value is 2.5 m/s² A(8) and the limit value is 5 m/s² A(8).

Whole-body vibration: EU action value is 0.5 m/s² A(8) and the exposure limit value is 1.15 m/s² A(8) or a VDV of 21 m/s^1.75.

Report the instrument class, calibration record, time weighting, frequency weighting, measurement duration, and meteorological conditions so results can be reproduced.

State the standard or guideline used (for example ISO 1996-2 or ANSI S1.4) and the metric (LAeq, Lden, LAmax); mixing metrics without labeling them is misleading.

Measurement uncertainty should be reported; typical expanded uncertainty for environmental LAeq is about 2–3 dB, and compliance decisions should account for it.

Conflicts of interest must be disclosed; an assessor who also designs the mitigation should state that relationship in the report.

Do not present modeled results as measured data; identify model name, version, input assumptions, and validation against measurements.

Retain raw data and calibration certificates for the period required by the client or regulator; chain of custody matters if results may be contested.

When results exceed a criterion, state the exceedance in dB and the affected period; avoid qualitative language such as "slightly above" without numbers.

Peer review and independent verification are appropriate for large projects; document reviewer identity and scope.

Reference values: p0 = 20 µPa, I0 = 1 pW/m², W0 = 1 pW; these are the anchors for all dB conversions.

Sound pressure and intensity are related by I = p²/(ρc); at 20 °C and 101.3 kPa, ρc ≈ 415 N·s/m³.

A 10 dB increase is perceived as roughly a doubling of loudness; a 3 dB change is barely perceptible in steady broadband noise.

Combining incoherent sources: L = 10 log10(10^(L1/10) + 10^(L2/10)); coherent sources require amplitude addition before conversion.

Wavelength λ = c/f; at 20 °C, c ≈ 343 m/s, so 100 Hz has λ ≈ 3.43 m and 1 kHz has λ ≈ 0.343 m.

Speed of sound in air rises with temperature: c ≈ 331.3 + 0.606·T (°C) m/s.

Standing waves form when a dimension is a multiple of λ/2; room modes cause uneven low-frequency response below the Schroeder frequency.

Loudness level in phons equals the SPL of a 1 kHz tone judged equally loud; sones are proportional to loudness, with 1 sone = 40 phon.

Microphone height for environmental measurements is typically 1.2–1.5 m above ground for facade or free-field assessment; report the actual height used.

Free-field versus diffuse-field microphone correction: apply the appropriate correction when the sound field differs from the microphone's design field.

A calibrated pistonphone produces a known level (commonly 94 dB at 1 kHz); record the pre- and post-measurement calibration values.

Background noise correction: if the background is 3 dB below the total, the source level is uncertain; a 10 dB difference gives a 0.4 dB correction.

Leq over a period can be computed from short-term samples only if the sampling is representative; report sampling interval and weighting.

Wind noise: use a windscreen and orient the microphone; discard data with wind speeds above the manufacturer's limit (often 5 m/s for a 90 mm screen).

Tone assessment: use a method such as ISO/PAS 20065 or the ANSI S1.13 tone-to-noise ratio; a prominent tone may warrant a penalty of up to 5–6 dB.

Vibration measurement: mount accelerometers rigidly and consider the mounted resonance; a mounting resonance below 3× the measurement range causes errors.

TWA from task durations: TWA = 16.61·log10(D/100) + 90 for the OSHA 5 dB exchange rate, where D is the dose in percent.

For a 3 dB exchange rate, TWA = 85 + 10·log10(D/100) with D referenced to 85 dBA for 8 hours.

Partial-period exposure: compute each task's contribution C/T and sum; if the sum exceeds 1.0, the exposure exceeds the criterion.

Hearing protector selection: choose protectors that bring exposure below 85 dBA; over-protection can impair communication and warning signal detection.

Audiometric follow-up: a confirmed STS requires retest within 30 days and notification; the employer must fit or refit hearing protectors and provide training.

Recordkeeping: OSHA requires noise exposure records for 2 years and audiometric records for the duration of employment plus 30 years.

Engineering controls: enclosures, silencers, and damping are preferred; administrative controls such as rotation are temporary and must not be used to avoid feasible engineering controls.

Training must cover effects of noise, purpose of protectors, fitting, and audiometric testing; repeat annually.

ISO 1996-2 covers determination of environmental noise levels; ISO 1996-1 covers descriptors and basic quantities including Lden and Lnight.

LAmax is the maximum A-weighted level with a specified time weighting (often Fast); report the weighting because Fast and Impulse give different maxima.

Percentile levels: L10, L50, and L90 describe the distribution; L90 is often used as a background indicator and L10 as a peak-traffic indicator.

Modeling inputs: source emission levels, receiver coordinates, ground impedance, barrier geometry, and meteorology; document each input source.

Barrier design: place the barrier close to the source or receiver, ensure it breaks line of sight, and avoid gaps; a small gap can severely reduce insertion loss.

Construction noise: many jurisdictions set limits by time period and by sensitive receptor type; report the applicable limit alongside measured levels.

Wind turbine noise: amplitude modulation and low-frequency content are assessed separately from LAeq; tonal and impulsive penalties may apply.

Compliance reporting should state the averaging period, the number of valid samples, and whether unfavorable meteorological conditions were included.

Source control options: quieter equipment, reduced speeds, damping treatments, and improved maintenance; a 3 dB reduction requires halving the sound power.

Enclosure design: use absorptive lining, minimize openings, and seal penetrations; an enclosure's insertion loss is limited by leaks and by structure-borne paths.

HVAC noise: use duct silencers, flexible connectors, and lined ducts; airflow-generated noise increases roughly with the sixth power of velocity.

Vibration isolation selection: choose a mount whose natural frequency is at most one-third of the lowest forcing frequency; verify with the static deflection.

Damping reduces resonant response; constrained-layer damping is effective for thin panels and plates.

Commissioning: verify mitigation performance with before/after measurements at the same positions and conditions; report the achieved insertion loss.

Maintenance matters: worn bearings and loose panels raise noise; periodic inspection preserves the designed performance.

Cost-effectiveness: prioritize measures by dB reduction per unit cost and by the number of people affected.

Annoyance increases with Lden but also depends on the character of the noise: tonal, impulsive, or low-frequency noise produces more annoyance at the same level.

Low-frequency noise: below about 100 Hz, A-weighting underestimates effects; use C-weighted or linear levels and specific criteria such as the Swedish or Danish low-frequency limits.

Speech interference: the speech interference level (SIL) is the average of octave-band levels at 500, 1000, 2000, and 4000 Hz; an SIL around 45 dB allows relaxed conversation at 1 m.

Vibration comfort: ISO 2631-1 provides comfort reactions and uses frequency weightings Wk, Wd, and Wf depending on axis and posture.

Combined exposure to noise and vibration can increase discomfort; assess both when the workplace involves both.

Children and the elderly are generally more sensitive to noise; criteria for schools and hospitals are typically stricter than for residential areas.

Tonal penalty: a clearly audible tone may add 5 dB to the assessed level in some national schemes; document the method used.

Reporting human response: distinguish measured exposure from predicted response and avoid asserting health outcomes without evidence.