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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

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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

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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
+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

Alan Dec 12, 2018