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 Loudness is measured in decibels; for instance, the lowest sound that a human can detect has a sound intensity of  10−12watts per square meter. 

Decibel levels are calculated using the following logarithmic equation: L(I)=10log⁡(I/10−12) where II is the intensity of sound in watts per square meter. 

The sound of an MP3 player has a maximum volume of 125 decibels. Determine the intensity of this sound to the nearest thousandth. 

The intensity is  _______________watts per square meter.

 Dec 12, 2018

Best Answer 

 #1
avatar+27529 
+2

L(I)=10log⁡(I/10−12)

 

L(I) = 125, so  125 = 10log⁡(I/10−12)

 

Divide both sides by 10

12.5 = log⁡(I/10−12)

 

Antilog both sides:

1012.5 = I/10−12

 

Multiply both sides by 10-12 

10-121012.5 = I

 

Using the fact that 10a10b = 10a+b we have:

I = 100.5   or  I = √10

 Dec 12, 2018
 #1
avatar+27529 
+2
Best Answer

L(I)=10log⁡(I/10−12)

 

L(I) = 125, so  125 = 10log⁡(I/10−12)

 

Divide both sides by 10

12.5 = log⁡(I/10−12)

 

Antilog both sides:

1012.5 = I/10−12

 

Multiply both sides by 10-12 

10-121012.5 = I

 

Using the fact that 10a10b = 10a+b we have:

I = 100.5   or  I = √10

Alan Dec 12, 2018

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