Decibel formula1/31/2024 ![]() The sound intensity in the car is 57.8 dB. Therefore, by putting on both layers of ear protection, the worker reduces the sound intensity by a factor of 3162. Here dB stands for decibels, log stands for logarithm. The ratio of the full sound intensity to the reduced sound intensity the worker hears is approximately 3162. This equation can be represented by: The intensity of sound in decibels is 10 dB × log (II0). The ratio of the full sound intensity to the reduced sound intensity, expressed as Watts per meter squared is. To identify which sound is which, they can be labeled with the index values 1 and 2: ![]() Using this mathematical formula for logarithms, the decibel formula can be rearranged to solve for I: The mathematical formula for logarithms needed is: This problem can be solved by finding I for decibel values of 120 dB and 85.0 dB, and then dividing the full intensity by the reduced intensity. What is the ratio of the full sound intensity to the reduced sound intensity the worker hears?Īnswer: The decibel scale is logarithmic, and so a small drop in the decibel intensity means a much larger drop in the intensity expressed as. This reduces the intensity of the sound he hears from 120 dB to 85.0 dB. The sound intensity in the car is approximately 57.8 dB.Ģ) A worker uses double ear protection, both earplugs and earmuffs, to reduce the intensity of the sound of a jackhammer. The intensity of the sound in decibels can now be found using the decibel formula: "Micro" means, and so the sound intensity in the car is: What is this sound intensity in decibels?Īnswer: The sound intensity in the car is expressed in micro-Watts per meter squared.
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