Basic Concepts in Engineering Acoustics
Definition
Acoustics is defined as the science of sound.
Sound Characterization
| Qualitative (Perceived) | Quantitative (Measured) |
|---|---|
| Loudness | Sound Pressure Level [dB] |
| Pitch | Frequency [Hz] |
| Duration | Time [s] |
Sound Level
According to Weber’s Law, perceptions (vision, hearing, taste, touch, and smell) varies logarithmically with the excitation stimulus. Leading to logarithmic expression of sound pressue level.
Human Hearing Threshold
| Parameter | Lower Limit | Upper Limit |
|---|---|---|
| Pressure | 20 μPa (Threshold of Hearing) | 200 Pa (Threshold of Pain) |
| SPL (ref 20 μPa) | 0 dB | 140 dB |
| Frequency | 20 Hz | 20,000 Hz |
| Most Sensitive f (Human) | 500 Hz | 5,000 Hz |
Human Perception of SPL in dB
| Change in SPL (dB) | Loudness Perceived |
|---|---|
| 3 | Perceivable |
| 5 | Noticeable difference |
| 10 | Twice as loud |
| 15 | Significant difference |
| 20 | Four times as loud |
Addition of SPL
| X + (dB): | Result (dB) |
|---|---|
| X | X + 3 |
| X + 1 | X + 3.5 |
| X + 2 | X + 4.1 |
| X + 3 | X + 4.8 |
| X + 4 | X + 5.5 |
| X + 5 | X + 6.2 |
| X + 6 | X + 7.0 |
| X + 7 | X + 7.8 |
| X + 8 | X + 8.6 |
| X + 9 | X + 9.5 |
| X + 10 | X + 10.4 |
| X + 11 | X + 11.3 |
| X + 12 | X + 12.3 |
| X + 13 | X + 13.2 |
| X + 14 | X + 14.2 |
| X + 15 | X + 15.1 |
| X + 16 | X + 16.1 |
Sound Level Weightings
Frequency weighting system was standardized by the International Electrotechnical Commission (IEC)
| Weighting | Description |
|---|---|
| A | Initially introduced for low level (loudness) sounds (up to 40 phons). Most commonly used as a rough estimate of the frequency sensitivity of human hearing. |
| B | To treat higher-level (loudness) sound. (Disused) |
| C | Takes better account of low-frequency sound levels. Used in few occupational noise regulations. |
| D | To treat higher-level (loudness) sound. Devoted to aircraft sound level measurements. (Disused) |
| Z (zero) | No weighting. |
For more information, NTi-Audio provided a good reference for further reading and correction factors for Octave and 1/3 Octave Bands.
Some reference values on A-weighted SPLs.
| SPL (dBA) | Interpretation |
|---|---|
| 18 | Woodland area without wind (and without birds singing either! |
| 30 | Empty cinema projection room. |
| 45 | Workstation with the desktop computer fan running. |
| 70 | Busy street. |
| 90 | Airport façade with a plane maneuvering at the pier. |
| 140 | 5 m from a jet engine |
Since it is possible to achieve a given weighted value with rather different spectrum shapes, one usually specifies noise limits using simultaneously a global A-weighted sound level value and a frequency contour featuring higher levels in the lower-frequency range than in the higher-frequency range.
E.g.: A-weighted SPL for 100 dB (@ 1000 Hz) = 126 dB (@ 63 Hz)
Common Noise Weighting Curves (Countours)
| Contour | Description | Standards |
|---|---|---|
| Noise Criterion (NC) | Less stringent, covering frequency range of (62.5 - 8000) Hz | ANSI S12-2-2008 |
| Noise Rating (NR) | More stringent, covering frequency range of (31.5 - 8000) Hz | ISO 1996:1971 |
Equivalent Sound Levels and Statistical Sound Levels
Equivalent Sound Pressure Level, 
Acoustic measurements are temporal fluctuations of pressure. To gauge or quantify the measurements easily, equivalent sound level, Leq, is used. For A-weighted Leq, the quantity is denoted as LAeq.
Leq represents a non-fluctuating signal containing as much acoustic energy as the signal under study over the period of time considered.
(Source: NI Sound and Vibration Software: Leq Sound Level Meaning)
Statistical Sound Level, 
In actual, a 65 dB(A) LAeq value can be reached close to a major highway where it is a continuous rumble, but it can also be reached close to a country road if a single motorcycle passes by
Although with Leq, it is easier to make sense of the acoustic measurements, the temporal fluctuations of a noise could be very different with the same Leq. This is when people use the notion of statistical sound levels, Lx.
Lx is the sound level reached or exceeded for x % of the analysis time.
Commonly used Lx values are:
| Lx | Meaning | Interpretation |
|---|---|---|
| L10 | Sound level reached or exceeded for 10% of the analysis time. | Quantify the highest noise level taken. Used for measuring impact or short and transient burst of noise (e.g.: traffic noise). |
| L50 | Sound level reached or exceeded for 50% of the analysis time. | Usually less than Leq for fluctuating noise. |
| L90 | Sound level reached or exceeded for 90% of the analysis time. | Quantify the lowest noise level taken. Used for measuring background or ambient noise. |
For further information, Pulsar Instruments has an article which explains statistical sound levels in greater depths.
References
[1] M. Asselineau, Building Acoustics. Boca Raton, Florida: CRC Press, 2015.
[2] D. A. Bies, C. H. Hansen, and C. Q. Howard, Engineering Noise Control, 5th ed. Boca Raton, Florida: CRC Press, 2017.