SOLUTION: ASAP HELP!(^)I use this symbol to represent exponents
I have a question, if the loudness level of a sound, D, in decibels, is given by the formula D= 10 log (10^12 I) where I is
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Question 80892: ASAP HELP!(^)I use this symbol to represent exponents
I have a question, if the loudness level of a sound, D, in decibels, is given by the formula D= 10 log (10^12 I) where I is the intensity of the sound, in watts per meter^2. Decibel levels range from 0, a barely audible sound, to 160, a sound resulting in a ruptured eardrum. What is the decibel level of a normal conversation, 3.2 x 10^-6 watt per meter^2?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If your decibel formula is
)
Simply plug in 
into I
))
Group the terms 
and 
(3.2)))
Since we're multiplying two like bases with exponents we can add the exponents
}(3.2)))
))
add the exponents
+\log_{10}(3.2)))
Break up the logs by using this identity =\log(x)+\log(y))
We can clearly see that =6)
(since this is always true =x)
) so it reduces to
))
Now use your calculator to find )
. It comes to 0.50515
So our problem reduces further to
)
)
Add
Multiply
So an intensity of 3.2 x 10^-6 watt per meter^2 means the decibel measure is about 65.015 decibels. For more problems dealing with decibels check out this decibel calculator. You'll need to use the calculator on the far right.
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