Solve the problem.
-Use the formula $L = 10 \cdot \log \frac { \mathrm { I } } { \mathrm { I } }$, where the loudness of a sound in decibels is determined by I, the number of watts per square meter produced by the sound wave, and I $0 = 10 ^ { - 12 }$ watts per square meter. What is the intensity of a noise measured at $56 \mathrm { db }$ ?
A) $2.7 \times 10 ^ { 14 }$ watts per square meter
B) $3.98 \times 10 ^ { - 7 }$ watts per square meter
C) $3.98 \times 10 ^ { - 6 }$ watts per square meter
D) $5.6 \times 10 ^ { - 10 }$ watts per square meter

Question

Quizplus · Accepted Answer

First, we can rearrange the formula to solve for I:
$$L = 10 \cdot \log \frac { \mathrm { I } } { \mathrm { I } }$$
$$10^{L/10}=\frac{I}{I_0}$$
$$I=I_0\cdot10^{L/10}$$
Now we can plug in the given value for L:
$$I=I_0\cdot10^{56/10}$$
$$I=10^{-12}\cdot10^5.6$$
$$I=3.9810717055\times10^{-7}\approx\boxed{B}$$

Solve the Problem L=10⋅log⁡IIL = 10 \cdot \log \frac { \mathrm { I } } { \mathrm { I } }L=10⋅logII​

Solve the Problem $L = 10 \cdot \log \frac { \mathrm { I } } { \mathrm { I } }$