Given that $I_{0}=10^{-12}$ watts/meter ${ }^{2}$, what is the decibel level of a sound, for which the sound intensify is 0.0006 watts/meter ${ }^{2}$ Round your answer to the nearest integer.

Answer

Step 1 ：We are given that the reference intensity, \(I_{0}\), is \(10^{-12}\) watts/meter\(^{2}\) and the intensity of the sound, \(I\), is 0.0006 watts/meter\(^{2}\).

Step 2 ：We can calculate the decibel level of the sound using the formula: \(dB = 10 \times \log_{10}(I / I_{0})\).

Step 3 ：Substituting the given values into the formula, we get: \(dB = 10 \times \log_{10}(0.0006 / 10^{-12})\).

Step 4 ：Solving the above expression, we get \(dB = 87.78151250383644\).

Step 5 ：Rounding the above result to the nearest integer, we get \(dB = 88\).

Step 6 ：Final Answer: The decibel level of the sound is \(\boxed{88}\).