22-Mec-B11 Acoustics and Noise Control · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2017 — 16-Mec-B11 Acoustics and Noise Control; 3 hours; CLOSED BOOK (one approved Casio or Sharp calculator). Seven questions of equal value (20 marks each); FIVE questions constitute a complete paper. All seven are solved here so the set works as a study resource.
Reference texts. D. A. Bies, C. H. Hansen and C. Q. Howard, Engineering Noise Control, 5th ed. (CRC Press) — the standard reference for this exam code; L. L. Beranek and I. L. Vér, Noise and Vibration Control Engineering, 2nd ed. (Wiley); L. E. Kinsler, A. R. Frey, A. B. Coppens and J. V. Sanders, Fundamentals of Acoustics, 4th ed. (Wiley); CSA Z107 series and the provincial OH&S noise regulations for the Canadian occupational-exposure context.
Units and constants used throughout. Reference pressure $p_{\text{ref}}=20\ \mu\text{Pa}$; reference power $W_{\text{ref}}=10^{-12}\ \text{W}$; reference intensity $I_{\text{ref}}=10^{-12}\ \text{W/m}^2$. Where a question does not state the air temperature, air at $20\ {}^\circ\text{C}$ is assumed: $c=343\ \text{m/s}$, $\rho_0 c = 413\ \text{rayl}$. Question 3 states its own values and they are used there.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Given. Ten standard acoustic terms (A–J) and ten standard definitions (1–10) drawn from the ISO/ANSI vocabulary of acoustics, plus four discussion topics spanning signal analysis, wave behaviour and instrumentation.
Find. The one-to-one matching of terms to definitions, and a reasoned discussion of the four Part B topics with engineering examples.
Approach. Part A is settled by reading each definition for its defining physical quantity (a ratio of powers, an energy average, a frequency interval) rather than by keyword matching, because several definitions share vocabulary; Part B is answered as connected prose, each topic tied to how it is actually used in a noise-control measurement.
| Term | Definition | Why it is the unique match |
|---|---|---|
| A — frequency weighting | 3 | A standardized filter shape applied to the signal; it is the generic concept of which A- and C-weighting are the two named instances. |
| B — hourly average sound level ($L_{8hr}$) | 5 | The symbol given is the eight-hour A-weighted average, i.e. the shift-long exposure descriptor; definition 5 is the only one that names an 8-hour averaging period. |
| C — C-weighted sound level | 6 | Definition 6 is the only one that names the c-weight network on the meter. |
| D — background noise | 8 | Definition 8 is the only one framed as everything other than the sound of interest. |
| E — average sound pressure level ($L_{eq}$) | 1 | Definition 1 is the equal-energy (equivalent continuous) level: the steady level carrying the same energy as the fluctuating one. |
| F — octave | 9 | An octave is a frequency interval, defined by the 2:1 ratio; definition 9 is the interval, definition 7 is the spectrum built from it. |
| G — sound intensity ($I$) | 10 | Definition 10 is a directional power-per-unit-area, in W/m$^2$ — a vector quantity, unlike sound power. |
| H — sound power level ($L_w$) | 4 | Definition 4 is $10\log_{10}(W/W_{\text{ref}})$ with the $10^{-12}\ \text{W}$ reference; note the source's "$10^{12}$" is a typesetting slip for $10^{-12}$ W. |
| I — octave-band spectrum | 7 | Definition 7 is a spectrum whose bands are one octave wide — the display, not the interval. |
| J — A-weighted sound level ($L_A$) | 2 | Definition 2 is the level measured through the A network, in dB(A). |
Two pairs are deliberately confusable and are worth stating explicitly. F/I separates the interval (a 2:1 frequency ratio) from the spectrum plotted in bands one octave wide; G/H separates intensity, which is directional and measured per unit area, from sound power level, which is a property of the source alone and independent of where you stand. The 8-hour descriptor B is likewise not a synonym for $L_{eq}$: $L_{eq}$ is defined over any stated period, whereas the shift descriptor fixes that period at eight hours and fixes the weighting at A.
(i) Time domain, frequency domain and the Fourier series. A sound is completely described either as a pressure history $p(t)$ or as the set of amplitudes and phases of the sinusoids that sum to it; the two descriptions carry identical information and the Fourier series is the bridge between them for any periodic signal, $p(t)=\sum_{n} A_n\cos(n\omega_0 t+\phi_n)$. The distinction matters because noise control is almost always frequency-selective: a barrier, an absorber, a silencer and the human ear all behave differently at 125 Hz than at 4 kHz. A gearbox whine, for example, looks like an anonymous rumble in the time domain, but its spectrum shows a line at tooth-meshing frequency and its harmonics, which immediately identifies the gear mesh as the source and tells you the treatment must be tuned there. The time domain remains indispensable for transients — impacts, blasts and door slams — where peak pressure and rise time, not a spectrum, govern hearing damage risk.
(ii) Standing waves, the electrical–acoustical analogy and acoustic impedance. A standing wave arises when an incident and a reflected wave of the same frequency superpose, producing fixed nodes and antinodes; in a duct or a room this creates positions where a measurement can be 20 dB wrong, and modal "boom" at the room's axial frequencies. Acoustic impedance, $Z=p/u$ (specific) or $p/U$ (acoustic), is the ratio that decides how much of a wave reflects at a discontinuity: reflection is governed by the impedance mismatch, which is why an open pipe end reflects strongly even though nothing solid is there. The electrical–acoustical analogy maps pressure to voltage, volume velocity to current, compliance to capacitance and inertance to inductance, so an entire muffler or loudspeaker enclosure can be drawn and solved as a lumped circuit. That analogy is what makes an expansion-chamber muffler designable on paper: it is an acoustic low-pass filter, and its transmission loss follows directly from the impedance mismatch at each area change.
(iii) Frequency response function. The FRF, $H(\omega)=Y(\omega)/X(\omega)$, is the complex ratio of output to input as a function of frequency, and it characterizes a linear system independently of whatever signal happens to be driving it. In noise and vibration work it is the everyday measurement: hammer a machine frame while measuring force and acceleration, and the resulting accelerance FRF reveals the natural frequencies, damping and mode shapes that determine which excitation frequencies will be amplified. Because $H(\omega)$ carries phase as well as magnitude, it also tells you how a structure responds, which is what allows a resonance to be shifted by stiffening rather than merely damped. A companion measurement, the coherence function, reports how much of the measured output is genuinely caused by the measured input and so warns when the FRF is contaminated by an unmeasured source.
(iv) The diaphragm in a condenser microphone. The diaphragm is one plate of a capacitor whose other plate is a fixed, perforated backplate; sound pressure deflects the diaphragm, changing the gap and hence the capacitance, and with the capacitor held at a constant polarizing charge that capacitance change appears directly as an output voltage. Its mechanical design sets essentially every performance figure of the microphone: tension and mass fix the fundamental resonance and hence the upper limit of the flat frequency response, area fixes the sensitivity, and stiffness fixes the dynamic range. A precision measurement microphone therefore uses a thin, highly tensioned nickel diaphragm to push its resonance above 20 kHz and keep the response flat across the audible band, and a capillary vent behind it equalises static pressure so barometric and temperature changes do not bias the reading.
| Part | Answer |
|---|---|
| Part A matching | A–3, B–5, C–6, D–8, E–1, F–9, G–10, H–4, I–7, J–2 |
| Part B | Four topics discussed with engineering examples (see above) |
