![]() ![]() 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. The ratio of the full sound intensity to the reduced sound intensity the worker hears is approximately 3162. The scale is dened by 10log I I0 (6) where is in dB. The dB scale was invented by telephone engineers, and a deci Bell is 1/10 th of a Bell, which we dene below. The ratio of the full sound intensity to the reduced sound intensity, expressed as Watts per meter squared is. The decibel scale is useful in dening ratios of numbers, which may vary over many orders of magnitude (powers of 10). 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. The number of decibels increases by 10 for a factor of 10 increase in intensity. Because the decibel scale is logarithmic, it changes by an additive constant when the intensity as measured in W/m2 changes by a multiplicative factor. 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. The decibel scale is a logarithmic scale for measuring the sound intensity level. 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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