If I₀ = 10 ^- ¹² W/m² is the threshold of hearing, a sound with intensity I₁ = 10 ^- ¹⁰ W/m² will give a certain decibel level. Suppose a new sound has an intensity I₂ = I₁²/I₀. What is the new decibel level? A) 40 B) 20 C) 10,000 D) It will square the decibel level.

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Quizplus · Accepted Answer

The decibel level is calculated using the formula 10 * log10(I/I0). For I1, the decibel level is 20 dB. For I2 = I1^2/I0, the decibel level is 10 * log10((I1^2/I0)/I0) = 10 * log10(I1^2/I0^2) = 2 * 10 * log10(I1/I0) = 2 * 20 = 40 dB.

If I0 = 10 - 12 W/m2 Is the Threshold

If I₀ = 10 ^- ¹² W/m² Is the Threshold