Solving a Decibel Noise Equation
Date: 05/23/2000 at 17:58:23 From: Ian Hazelden Subject: Noise Equations How do you rearrange the formula 50 = 94.5 - 20log(r) - 8 to solve for r?
Date: 05/23/2000 at 18:04:13 From: Doctor Douglas Subject: Re: Noise Equations Hi Ian, Thanks for sending your question to Ask Dr. Math. Since you write "noise" equations in the subject line, I presume that you are talking about sound intensity and that the logarithm is the appropriate one for decibels (it is the log base 10.) With that, we rearrange the formula that you gave: 50 = 94.5 - 20 log(r) - 8 20 log(r) = 94.5 - 8 - 50 20 log(r) = 36.5 log(r) = 36.5 / 20 = 1.825 Now raise ten (it could be any number, but we are choosing to use log base 10) to both sides: log(r) 1.825 10 = 10 1.825 r = 10 = 66.83 - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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