To learn the properties of logarithms and how to manipulate them when solving so

Question

To learn the properties of logarithms and how to manipulate them when solving sound problems.
The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or m W/m^2.

The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10^{-12}; m W/m^2, and we begin to feel pain when the intensity reaches 1 m W/m^2 . Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level beta, which is measured in decibels ( m dB). For a given sound intensity I, beta is found from the equation

eta=(10;{ m dB})logleft( rac {I}{I_0} ight),

where I_0=1.0 imes 10^{-12}; { m W/m^2}.


Use this technique to find a formula for the intensity I of a sound, in terms of the sound level beta and the reference intensity I_0. There will be a quantity (10 { m dB}) involved in your calculations. When you enter your answer, leave off the unit m dB.
Express your answer in terms of beta and I_0.

Explanation / Answer

= 10 log (I/I_0) where I_0 = 10^-12 W/m^2

(/10) = log (I/I_0)

I/I_0 = 10^(/10)

I = I_0*10^(/10)

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