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Sound intensities, I, are often compared with the threshold of human hearing, I_0, which is about 10^-12 watts per meter squared. The relative intensity, R, of a sound is given by the equation: R = 10log(I/I_0)

 

 

i. The intensity of a whisper is about 300 times as loud as the threshold of human hearing. Find the relative intensity, R, of a whisper in decibels.

 

 

ii.  Suppose a burglar alarm has a rating of 120 decibels. Compare this intensity to the threshold of human hearing.

 Mar 12, 2019
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1.  I/I0 = 300, so R = 10log10(300) decibels

 

2. Rearrange expression for R to get I/I0 = 10(R/10)  Substitute R = 120 in this.  Multiply by I0 if you want the result in watts per meter2.

 Mar 12, 2019
edited by Alan  Mar 12, 2019

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