Use the formula $\mathrm { D } = 10.0 \log ( \mathrm { S } / \mathrm { S } 0 )$ where the loudness of a sound in decibels is determined by S, the number of
$\text { watt/m² }$ produced by the soundwave, and $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 } \mathrm { watt } / \mathrm { m } ^ { 2 }$ What is the intensity in $\text { watt/m² }$ of a
noise measured at 40 decibels? (Round to the nearest tenth.)
A) $1.0 \times 10 ^ { - 7 } \mathrm { watt } / \mathrm { m } ^ { 2 }$
B) $4 \times 10 ^ { - 10 } \mathrm { watt } / \mathrm { m } ^ { 2 }$
C) $1.0 \times 10 ^ { - 8 } \text { watt } / \mathrm { m } ^ { 2 }$
D) $5.5 \times 10^{13} \mathrm { watt } / \mathrm { m } ^ { 2 }$

Question

Use the formula $\mathrm { D } = 10.0 \log ( \mathrm { S } / \mathrm { S } 0 )$ where the loudness of a sound in decibels is determined by S, the number of
$\text { watt/m² }$ produced by the soundwave, and $\mathrm { S } _ { 0 } = 1.00 \times 10 ^ { - 12 } \mathrm { watt } / \mathrm { m } ^ { 2 }$ What is the intensity in $\text { watt/m² }$ of a 
noise measured at 40 decibels? (Round to the nearest tenth.)
A) $1.0 \times 10 ^ { - 7 } \mathrm { watt } / \mathrm { m } ^ { 2 }$
B) $4 \times 10 ^ { - 10 } \mathrm { watt } / \mathrm { m } ^ { 2 }$
C) $1.0 \times 10 ^ { - 8 } \text { watt } / \mathrm { m } ^ { 2 }$
D) $5.5 \times 10^{13} \mathrm { watt } / \mathrm { m } ^ { 2 }$

Quizplus · Accepted Answer

To find the intensity S, rearrange the formula: $ \mathrm{D} = 10.0 \log(\mathrm{S}/\mathrm{S}_0) $. For 40 decibels, $ 40 = 10 \log(\mathrm{S}/1.00 \times 10^{-12}) $. Solving gives $ \mathrm{S} = 1.0 \times 10^{-8} \text{ watt/m}^2 $.

Use the Formula D=10.0log⁡(S/S0)\mathrm { D } = 10.0 \log ( \mathrm { S } / \mathrm { S } 0 )D=10.0log(S/S0)

Use the Formula $\mathrm { D } = 10.0 \log ( \mathrm { S } / \mathrm { S } 0 )$