Sound Intensity Converter
Instantly convert sound intensity with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Sound Intensity Converter
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Formula: dB = 10 * log10(I / I_ref) where I_ref = 10^-12 W/m^2
Worked example โ 110 dB at 1m = 90 dB at 10m (0.001 W/m^2)
Formula
dB = 10 * log10(I / I_ref) where I_ref = 10^-12 W/m^2
Sound level in dB equals 10 times the log of intensity divided by the reference intensity (threshold of hearing). Sound pressure: dB = 20*log10(P/P_ref). Inverse square law: intensity drops 6 dB per distance doubling.
Worked Examples
Example 1: Concert Sound Level at Distance
Problem:A concert speaker produces 110 dB at 1 meter. What is the level at 10 meters?
Solution:dB at new distance = original dB - 20*log10(new_dist/original_dist) dB = 110 - 20*log10(10/1) dB = 110 - 20 = 90 dB Intensity = 10^-12 * 10^(90/10) = 10^-3 W/m^2
Result:110 dB at 1m = 90 dB at 10m (0.001 W/m^2)
Example 2: Combining Office Noise Sources
Problem:An office has 5 identical printers each producing 65 dB. What is the combined level?
Solution:Combined dB = single source dB + 10*log10(N) Combined = 65 + 10*log10(5) Combined = 65 + 6.99 = 71.99 dB Combined intensity = 5 * 3.162e-6 = 1.581e-5 W/m^2
Result:5 printers at 65 dB each = 72 dB combined
Frequently Asked Questions
What is the decibel scale and how does it measure sound?
The decibel (dB) scale measures sound intensity logarithmically relative to the threshold of human hearing (10^-12 W/m^2). The formula is dB = 10 * log10(I / I_ref). Because it is logarithmic, every 10 dB increase represents a tenfold increase in intensity. Normal conversation is about 60 dB, a lawn mower about 90 dB, and a jet engine about 140 dB. The scale compresses the enormous range of human hearing (from 0 dB to 140 dB) into manageable numbers.
How does sound intensity decrease with distance?
Sound intensity follows the inverse square law in free space: intensity decreases proportionally to 1/r^2, where r is distance from the source. This means doubling the distance reduces the intensity by a factor of 4, which corresponds to a 6 dB decrease. A speaker producing 90 dB at 1 meter will produce about 84 dB at 2 meters and 78 dB at 4 meters. Indoors, reflections from walls reduce this attenuation effect.
How do you add sound levels from multiple sources?
Sound levels in decibels cannot be added directly because the scale is logarithmic. Instead, convert each level to intensity, add the intensities, then convert back to dB. For N identical sources, the combined level is original dB + 10*log10(N). Two identical 80 dB sources produce 83 dB (not 160 dB). Ten identical sources add 10 dB. This is why doubling speakers only adds 3 dB rather than doubling the perceived loudness.
What sound levels are dangerous to hearing?
Occupational safety standards (OSHA and NIOSH) set exposure limits based on duration. At 85 dB, the recommended maximum exposure is 8 hours. For every 3 dB increase, the safe exposure time halves: 88 dB for 4 hours, 91 dB for 2 hours, 94 dB for 1 hour, and so on. At 100 dB (power tools), damage can occur in just 15 minutes. Sound above 120 dB causes pain, and 140 dB can cause immediate permanent hearing damage.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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