Given that $I_{0}=10^{-12}$ watts/meter ${ }^{2}$, what is the intensity of a sound for which the decibel level of the sound measures 115 ? Round off your answer to three decimal places.

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watts/meter 2

Step 1 ：The decibel level of a sound is given by the formula: \(dB = 10 * log_{10}(I/I_{0})\) where I is the intensity of the sound and \(I_{0}\) is the reference intensity. In this case, \(I_{0}\) is given as \(10^{-12}\) watts/meter^2. We are asked to find the intensity of a sound for which the decibel level is 115.

Step 2 ：We can rearrange the formula to solve for I: \(I = I_{0} * 10^{(dB/10)}\)

Step 3 ：We can substitute the given values into this formula to find the intensity of the sound. \(I_{0} = 1e-12\), dB = 115

Step 4 ：Calculate I: \(I = 1e-12 * 10^{(115/10)}\)

Step 5 ：Final Answer: The intensity of the sound is approximately \(\boxed{0.316}\) watts/meter^2.