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The level of sound (D), which is measured in decibels, is defined by the equation D=10log(I/10^-16), where I is the sound intensity measured in watts/cm². Determine the level in decibels of a sound that has an intensity I = 10^-6 watts/cm². I don't understand where to go after plugging in I.

The level of sound (D), which is measured in decibels, is defined by the equation D=10log(I/10^-16), where I is the sound intensity measured in watts/cm². Deter class=

Answer :

Step 1

Define terms

The equation is

[tex]D=10\times\log _{10}(\frac{I}{10^{-16}})[/tex]

D=level of sound(decibels)

I = sound intensity (watts/cm²)

Step 2

Substitute and find the value of D

[tex]\begin{gathered} I=10^{-6}wattspercm^2 \\ D=10\times\log _{10}(\frac{I}{10^{-16}}) \\ D=10\times\log _{10}(\frac{10^{-6}}{10^{-16}}) \\ D=\text{ 10}\times\log _{10}(10^{-6-(-16)}) \end{gathered}[/tex][tex]\begin{gathered} D=\text{ 10}\times\log _{10}(10^{10}) \\ D=10\text{ }\times10 \\ D=\text{ 100 decibels} \end{gathered}[/tex]

Hence the level in decibel D of the sound = 100 decibels

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