SOLUTION: Please HELP HELP!!! Please help explain and show what is the decibel level of a normal conversation,(square root of 10)- 3.2 x watt per meter^2?

Question 80761: Please HELP HELP!!! Please help explain and show what is the decibel level of a normal conversation,(square root of 10)- 3.2 x watt per meter^2?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
What is the decibel level of a normal conversation,(square root of 10)- 3.2 x watt per meter^2?
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I'm not sure what your problem is supposed to be. The opening statement asks what is the
decibel level of a normal conversation. After that you have written
.
(square root of 10)- 3.2 watts per meter^2?
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That is not a decibel level because the decibel level has units of decibels, not watts/m^2.
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The units of watts/m^2 sort of implies that you are to take the decibel level of normal
conversation and find the sound energy in that level of normal conversation.
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Normal conversation is about 65 decibels.
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The equation that defines the decibel level of sound is:
.

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in which D is the number of decibels; Log is Log operator to the base 10; is
the sound energy, in this problem it is the energy of the sound in normal conversation;
and is the energy of sound that is the lowest sound energy that can be heard.
The internationally accepted standard for is watts/m^2 ... the
least amount of sound energy that is audible.
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If you are to find , the sound energy of normal conversation, you can do so if
you say that the decibel level of normal conversation is 65 decibels. All you have to
do is use the equation that defines decibels and substitute the values for D and .
As was noted, D = 65 and . Substituting those two values into the
equation results in:
.

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Recall that by the rules of Logarithms, if you take the Logarithm of a fractional
term, an equivalent is the Logarithm of the numerator minus the Logarithm of the denominator.
Applying this rule to the equation above results in:
.

.
Also recall that by the rules of Logarithms, if you have the Logarithm of a quantity that
has an exponent, an equivalent is the exponent times the Log of just the quantity.
Apply this rule to the last term on the right side of the equation and you get:
.

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But, the Log to the base 10 of 10 is just 1. So, substitute 1 for Log(10) to get:
.

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Note that -(-12)*1 is just +12. Substitute this and the equation becomes:
.

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Multiplying out the right side results in:
.

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Subtract 120 from both sides to get:
.

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Divide both sides by 10 to find that:
.

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Convert this to exponential form and you have:
.

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Calculator time. Raise 10 to the -5.5 power and the answer is in scientific notation is:
.

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That means that:
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watts/m^2
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Hope that I guess correctly what this problem was asking you to do. If you have a value
for the decibels for normal conversation and you need to find the sound energy of normal
conversation, just use this method only substitute your db value in place of 65 and work
it out. You'll probably need to re-post this problem if I guessed wrong. If you do re-post,
clarify what you are looking for, what that last term involving watts/m^2 is, and any
other information you want considered.
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Hope this helps you to understand the problem a little better too.
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Cheers!
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