The intensity, or loudness, of a sound can be measured in decibels d cap b , according to the equation cap i times d cap b is equal to 10 log open bracket the fraction with numerator cap i and denominator cap i sub 0 close bracket , where cap i is the intensity of a given sound and cap i sub 0 is the threshold of hearing intensity. What is the intensity, in decibels, open bracket cap i times d cap b close bracket , when cap i is equal to 10 to the 32th power times open paren cap i sub 0 close paren ?
Substitute I = 10^32 I₀ into the equation: I/I₀ = 10^32. Then dB = 10 log₁₀(10^32) = 10 × 32 = 320. The intensity is 320 decibels, choice D.
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