Acoustics Calculator

You cannot simply add decibels because they are logarithmic. Convert each to linear power, add, then convert back. Two equal sources of 80 dB combine to 83 dB - not 160 dB. The formula is 10 times log10 of (10 to the power of dB1/10 plus 10 to the power of dB2/10). Adding a 90 dB source to an 80 dB source gives 90.4 dB because the quieter source contributes relatively little.

In a free field, sound drops by 6 dB each time the distance doubles (inverse square law). A source measuring 100 dB at 1 meter reads 94 dB at 2 meters, 88 dB at 4 meters and 82 dB at 8 meters. Indoors, reflections slow this decay - a typical office might see only 3-4 dB drop per doubling of distance due to reverberant sound.

OSHA permits 90 dBA for 8 hours with a 5 dB exchange rate. At 95 dBA the limit drops to 4 hours, and at 100 dBA only 2 hours. The more protective NIOSH standard uses 85 dBA for 8 hours with a 3 dB exchange rate. A typical rock concert at 110 dBA exceeds the OSHA limit in just 30 minutes and the NIOSH limit in under 2 minutes.

Divide the speed of sound by the frequency. At 20 degrees C in air (343 m/s), a 1000 Hz tone has a wavelength of 0.343 meters or about 34.3 cm. Bass frequencies are much longer - 50 Hz has a wavelength of 6.86 meters, which is why low-frequency sound is so difficult to block with thin walls or absorb with small acoustic panels.

Sustained exposure above 85 dBA risks permanent hearing damage. A normal conversation is about 60 dBA, a vacuum cleaner roughly 75 dBA and a gas lawn mower about 90 dBA. At 85 dBA, hearing protection or time limits should begin. Single impulse sounds above 140 dB peak (like gunfire at 160 dB) can cause immediate damage even with brief exposure.