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.

Guest 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:

10^{12.5} = I/10^{−12}

Multiply both sides by 10^{-12}

10^{-12}10^{12.5} = I

Using the fact that 10^{a}10^{b} = 10^{a+b} we have:

I = 10^{0.5} or I = √10

Alan Dec 12, 2018

#1**+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:

10^{12.5} = I/10^{−12}

Multiply both sides by 10^{-12}

10^{-12}10^{12.5} = I

Using the fact that 10^{a}10^{b} = 10^{a+b} we have:

I = 10^{0.5} or I = √10

Alan Dec 12, 2018