Noise Level Calculator

Sound level falls with distance because a fixed acoustic power spreads over an expanding surface. For a point source radiating into free space, intensity varies as one over distance squared, so level drops by 20 x log10(d2/d1), or 6 dB per doubling of distance. A long line source such as a haul road spreads over a cylinder instead and loses only about 3 dB per doubling. Because decibels are logarithmic, sources combine on an energy basis through Ltotal = 10 x log10(10^(L1/10) + 10^(L2/10)). Two equal sources add 3 dB, a source 10 dB quieter adds about 0.4 dB, and anything 15 dB down is effectively irrelevant. The dBA weighting approximates the reduced sensitivity of the ear to low frequencies, following the 40-phon equal-loudness contour, and the reference pressure for 0 dB sound pressure level is 20 micropascals. Free-field geometry is an idealization. Within roughly two source dimensions the machine is not a point and levels fall more slowly; indoors the reverberant field dominates beyond the critical distance and the distance relationship fails entirely. Over long paths ISO 9613-2 adds ground effect, atmospheric absorption that grows with frequency and falls with humidity, and meteorological corrections, since downwind or temperature-inversion conditions can raise received levels several decibels above a still-air prediction. Barrier attenuation depends on how far sound must diffract around the edge rather than on mass alone: practical site barriers deliver about 5 to 15 dB, a well-built barrier fully blocking line of sight rarely exceeds 20 dB, and a barrier with gaps or one that fails to break line of sight delivers close to nothing regardless of material.

The decibel originated in telephony rather than acoustics. Engineers at Bell Telephone Laboratories used the mile of standard cable as a transmission loss unit, then replaced it in the mid-1920s with the bel, named for Alexander Graham Bell, and quickly with the more practical decibel of one tenth that size, formalized around 1928 and 1929. Applying it to human hearing required knowing how loudness varies with frequency, which Harvey Fletcher and Wilden Munson supplied at Bell Labs in 1933 with their equal-loudness contours. Those curves became the A, B and C weighting networks written into the American Standards Association sound level meter standard of 1936, and A-weighting, originally intended only for quiet sounds, survived to become the general-purpose weighting used in essentially all occupational and environmental noise regulation. Outdoor propagation modeling developed alongside highway and industrial noise regulation. Zyun-iti Maekawa published his diffraction chart in 1968 relating barrier insertion loss to the Fresnel number, giving designers a usable way to predict screening from geometry, and it still underlies most barrier calculations. The Noise Control Act of 1972 and federal highway noise regulations drove development of FHWA traffic noise prediction models, culminating in the Traffic Noise Model released in 1998. Internationally, ISO 9613-2, published in 1996, standardized the engineering method for attenuation outdoors, assembling geometric divergence, ground effect, atmospheric absorption and screening into a single calculation, and it remains the reference for construction and industrial noise assessments.