Tools › Mechanical Design › Acoustics › Room Acoustics and Noise Control › Example
A 30 x 20 x 10 ft office: Sabine, Eyring and Millington reverberation times from the UFC 3-450-01 absorption table, the treatment area for T60 = 0.6 s, and the NC rating of an office machine at 10 ft
| Tool | Room Acoustics and Noise Control |
| Source | U.S. Department of Defense (2022). Unified Facilities Criteria: Noise and Vibration Control. UFC 3-450-01, Appendix C-2 to C-4 (room constant, Table C-4 absorption coefficients, Figure C-1 relative SPL, Tables C-5 and C-6), Chapter 3 Table 3-1 (NC design goals); Sabine, W. C. (1922). Collected Papers on Acoustics. Harvard University Press; Eyring, C. F. (1930). Reverberation Time in Dead Rooms. JASA 1, pp. 217-241. |
| Level | Undergraduate |
Problem
An office 30 ft long, 20 ft wide and 10 ft high has a heavy carpet on concrete (600 ft²), a 1/2-in gypsum-board ceiling (600 ft²), smooth plaster walls on lath (880 ft²), 100 ft² of ordinary window glass and a 20 ft² plywood door, six people and two empty chairs, air at 68 °F and 50 % RH. Find the absorption, mean coefficient and room constant by octave band, the Sabine, Eyring and Millington reverberation times, the area of a treatment (0.30 / 0.70 / 0.90 / 0.95 / 0.95 / 0.95) replacing the ceiling that brings the 500 Hz Sabine time to 0.6 s, and the level and NC rating at 10 ft from a machine of band power levels 68 66 64 62 60 58 54 50 dB (63 Hz to 8 kHz, Q = 2) against the open-plan office goal NC 40.
Inputs to Enter
- Room 30 x 20 x 10 ft; surfaces Floor carpet on concrete 600 ft², Ceiling gypsum board 1/2 in 600 ft², Walls plaster smooth on lath 880 ft², Windows window glass 100 ft², Door plywood 3/8 in 20 ft² (UFC Table C-4 coefficients)
- 6 people, 2 empty chairs; air 68 °F, 50 % RH (ISO 9613-1); target T60 0.6 s at the 500 Hz design band; treatment coefficients 0.30 0.70 0.90 0.95 0.95 0.95 on row 2 (ceiling)
- Source L_w 68 66 64 62 60 58 54 50 dB, Q = 2, receiver 10 ft, space type open-plan office (NC 40)
Answers
- 500 Hz: A = 600(0.14) + 600(0.05) + 880(0.06) + 100(0.18) + 20(0.17) + 6(4) + 2(0.22) = 212.6 ft², mean coefficient 0.0967, air 4mV = 4.6 ft², R = A/(1 − ᾱ) = 235.4 ft²
- Sabine T60 = 0.049 V/(A + 4mV) = 1.36 s (Eyring 1.29 s, Millington 1.29 s) at 500 Hz; 1.16 / 0.81 / 1.26 / 1.36 / 0.88 / 0.60 / 0.53 / 0.51 s from 63 Hz to 8 kHz; Schroeder frequency 179 Hz
- Treatment: A_req = 0.049 x 6,000 / 0.6 − 4.6 = 486.1 ft², ΔA = 273.5 ft², area = 273.5/(0.90 − 0.05) = 321.8 ft² of the 600 ft² ceiling (54 %); T60 0.60 s and R = 624 ft² with it; at 125 Hz the same treatment would need 12,789 ft² (not achievable), at 2 kHz and above the target is already met
- Sound field at 10 ft, 500 Hz: direct 44.3 dB, reverberant 54.6 dB, L_p = L_w + 10 log(Q/(4πr²) + 4/R) = 55.0 dB, critical distance 3.06 ft; receiver spectrum 60.2 56.7 56.6 55.0 51.1 47.4 43.2 40.2 dB, 56.7 dBA; NC 51 (tangent at 500 Hz; NC-55 the lowest curve not exceeded) against the NC 40 goal; with the treatment the 500 Hz level falls to 51.4 dB
Notes
The tool's default inputs are this room; press Submit. The room is illustrative (stated on the page); every value is a closed form checked by test_room_acoustics.php (534 checks) against an independent numpy script (References/Room-Acoustics/checks/), and the same library reproduces the UFC 3-450-01 worked tables: C-5 and C-6 (Figure C-1 relative SPL within 1 dB), C-54 (RC Mark II example to the printed digits, RC 35(LF), QAI 7.2), C-30 and C-31 (the cooling-tower example, the default of the noise-criteria sub-tool) and the STC values printed with Tables C-12, C-13 and C-17.