NEBB S&V CP cheat sheet

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

Decibel addition of incoherent levels: L_total = 10 log10(10^(L1/10) + 10^(L2/10) + ...); two equal levels sum to +3 dB, ten equal levels to +10 dB.

A-weighting approximates the 40-phon equal-loudness contour and de-emphasizes low frequencies; C-weighting is flatter and is used for high-level and low-frequency assessment.

Octave band center frequencies (base-10 series): 31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000, 16000 Hz; one-third-octave bands use the 10^(1/10) ratio series.

Band edge frequencies: f_lower = f_center/√2 and f_upper = f_center·√2 for octave bands; for one-third-octave bands the factor is 2^(1/6).

Level versus distance for a point source in a free field: Lp2 = Lp1 − 20 log10(r2/r1), i.e. −6 dB per doubling of distance; a line source loses 3 dB per doubling.

Directivity index DI = Lp(θ) − Lp(average) in dB; directivity factor Q = 10^(DI/10); a point source on a hard floor radiates into a half space with Q = 2.

Room constant R = S·ᾱ/(1 − ᾱ), where S is total surface area and ᾱ is the average absorption coefficient; reverberant field level rises as R decreases.

Reverberation time by Sabine: RT60 = 0.161 V/A (metric, V in m³, A in m² sabins); Norris-Eyring replaces the denominator with −S·ln(1 − ᾱ).

Vibration amplitude descriptors: displacement (m), velocity (m/s), acceleration (m/s²); for sinusoidal motion the peak values relate by v_peak = 2πf·d_peak and a_peak = (2πf)²·d_peak.

RMS of a sinusoid equals peak/√2 (≈0.707·peak); crest factor = peak/RMS, equal to √2 for a pure sine and higher for impulsive signals.

Vibration level in dB: Lv = 20 log10(a_rms/a0) with a0 = 1 µm/s² (ISO reference) or 10 µm/s² depending on the standard cited; velocity reference is 1 nm/s and displacement reference 1 pm.

Frequency weighting for human response: ISO 8041 defines Wk (vertical, z-axis) and Wd (horizontal, x/y-axis) weighting filters applied before overall level calculation.

Accelerometer mounting: stud mounting gives the highest mounted resonance; adhesive, magnetic, and probe-tip mounting progressively lower usable frequency range and can reduce high-frequency sensitivity.

Piezoelectric accelerometers cannot measure true static (0 Hz) acceleration; charge amplifiers or IEPE constant-current sources convert charge to voltage for acquisition.

High-pass filtering removes low-frequency drift and integration noise; integrating acceleration to velocity or displacement attenuates high-frequency content by 1/(2πf) per integration.

FFT resolution Δf = fs/N and total record duration T = 1/Δf; frequency resolution improves with longer acquisition time, not with higher sampling rate alone.

Overall RMS from a spectrum: a_rms = √(Σ a_i²) where a_i are the individual band or line RMS amplitudes; do not sum peak amplitudes.