Fundamentals of Acoustics and Vibration
This domain tests whether you can move fluently between pressure, level, frequency and energy, and whether you can tell which physical quantity a question is actually asking about.
Core relationships
- Sound pressure level: Lp = 20 log10(p/p0) with p0 = 20 µPa. Sound power level uses 10 log10(W/W0) with W0 = 1 pW; intensity level uses 10 log10(I/I0) with I0 = 1 pW/m².
- Free field: I = p²/(ρc), and ρc ≈ 415 Pa·s/m in air at 20 °C, so LI ≈ Lp − 0.1 dB. Treat them as numerically equal but know why.
- Wavelength λ = c/f, with c ≈ 343 m/s at 20 °C. An octave doubles frequency; a one-third-octave band has a ratio of 2^(1/3) ≈ 1.26.
- Levels add logarithmically: L_total = 10 log10(Σ 10^(Li/10)). Two equal sources give +3 dB; ten equal sources give +10 dB.
- For a sinusoid, RMS = peak/√2 (crest factor 1.414); Gaussian noise has a crest factor near 4, i.e. about 12 dB.
Worked example
A microphone reads 0.2 Pa RMS. Lp = 20 log10(0.2 / 2×10⁻⁵) = 20 log10(10 000) = 80 dB. A second, uncorrelated machine producing 74 dB is then started: total = 10 log10(10^8.0 + 10^7.4) = 10 log10(1.25×10^8) = 81.0 dB. The addition is only 1 dB, which is barely perceptible, even though the second machine carries 25 % of the total sound power.
Traps that cost marks
- Adding or arithmetically averaging dB values: the arithmetic mean of 80 and 90 dB is 85 dB, but the energy mean is 87.4 dB.
- Mixing peak and RMS values, or reporting sound power when the criterion is stated as sound pressure - the reference quantities and reference values differ.
- Assuming 6 dB per doubling of distance indoors, in a duct or near a reflecting façade; that is free-field point-source behaviour only.
- Using the 20 log10 form on a power-like quantity or the 10 log10 form on a pressure-like quantity.