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# Sound intensities help

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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 11, 2019

#1
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The intensity of whisper is 300 times of the threshold. That means $$I_{\text{whisper}} = 300I_0$$.

$$R_{\text{whisper}} = 10\log\left(\dfrac{300I_0}{I_0}\right) = 10\log 300 \approx 24.77\;\text{dB}$$

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Mar 12, 2019
#2
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$$120 = 10\log\left(\dfrac{I}{I_0}\right)\\ 120 = 10\log\left(\dfrac{I}{10^{-12}}\right)\\ 10^{12} = \dfrac{I}{10^{-12}}\\ I = 10^{24} \;\text{Wm}^{-2}$$

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Mar 12, 2019
#3
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This is a repeat of the question at https://web2.0calc.com/questions/algebra-help_38#r1