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.