Solve the problem.
-Use the formula $\beta = 10 \log \left( \mathrm { I } / \mathrm { I } _ { \mathrm { O } } \right)$, where the loudness of a sound in decibels is determined by $\mathrm { I }$, the number of Watts/ $/ \mathrm { m } ^ { 2 }$ produced by the sound wave, and $\mathrm { I } _ { \mathrm { O } } = 10 ^ { - 12 } \mathrm {~W} / \mathrm { m } ^ { 2 }$. What is the intensity in Watts/m² of a noise measured at 37 decibels? (Round to the nearest tenth.)
A) $4.0 \times 10^{13} \mathrm {~W} / \mathrm { m } ^ { 2 }$
B) $5.0 \times 10 ^ { - 9 } \mathrm {~W} / \mathrm { m } ^ { 2 }$
C) $5.0 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 }$
D) $3.7 \times 10 ^ { - 10 } \mathrm {~W} / \mathrm { m } ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the intensity $I$ in Watts/m² for a noise measured at 37 decibels, we use the given formula $\beta = 10 \log \left( \mathrm { I } / \mathrm { I } _ { \mathrm { O } } \right)$ and solve for $I$. Given $\beta = 37$ decibels and $\mathrm { I } _ { \mathrm { O } } = 10 ^ { - 12 } \mathrm {~W} / \mathrm { m } ^ { 2 }$, we rearrange the formula to solve for $I$: $I = 10^{(\beta/10)} \times \mathrm { I } _ { \mathrm { O } }$. Substituting the given values, $I = 10^{(37/10)} \times 10^{-12}$, which simplifies to $I = 10^{3.7} \times 10^{-12}$. Calculating this gives $I \approx 5.0 \times 10^{-9} \mathrm {~W} / \mathrm { m } ^ { 2 }$, rounding to the nearest tenth.

Solve the Problem β=10log⁡(I/IO)\beta = 10 \log \left( \mathrm { I } / \mathrm { I } _ { \mathrm { O } } \right)β=10log(I/IO​)

Solve the Problem $\beta = 10 \log \left( \mathrm { I } / \mathrm { I } _ { \mathrm { O } } \right)$