sound intensity model: l = 10log(i/i0) l = lo...
sound intensity model: l = 10log(i/i0) l = loudness, in decibels (db); i = sound intensity, in watts/m2; i0 = 10-12 watts/m2 the loudness of a jack hammer is 96 db. its sound intensity is about 0.004. the loudness of a compactor is 94 db. its sound intensity is about 0.0025. complete the sound intensity of the jack hammer is about 1.6 times the sound intensity of the compactor. complete the loudness of a pile driver is 112 db. about how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? round to the nearest ten. done
Answer
# Explanation:
## Step1: Find sound - intensity formula
Given $L = 10\log(\frac{I}{I_0})$, we can solve for $I$:
$\frac{L}{10}=\log(\frac{I}{I_0})$. By the definition of logarithms, $10^{\frac{L}{10}}=\frac{I}{I_0}$, so $I = I_0\times10^{\frac{L}{10}}$.
## Step2: Calculate sound - intensity of jack - hammer
For the jack - hammer with $L_{jh}=96$ dB and $I_0 = 10^{- 12}$ watts/m², $I_{jh}=10^{-12}\times10^{\frac{96}{10}}=10^{-12}\times10^{9.6}=10^{-12 + 9.6}=10^{-2.4}\approx0.004$ watts/m².
## Step3: Calculate sound - intensity of pile driver
For the pile driver with $L_{pd}=112$ dB, $I_{pd}=10^{-12}\times10^{\frac{112}{10}}=10^{-12}\times10^{11.2}=10^{-12 + 11.2}=10^{-0.8}$ watts/m².
## Step4: Calculate the ratio of sound - intensities
The ratio $\frac{I_{pd}}{I_{jh}}=\frac{10^{-0.8}}{10^{-2.4}}$. Using the rule $\frac{a^m}{a^n}=a^{m - n}$, we have $\frac{10^{-0.8}}{10^{-2.4}}=10^{-0.8+2.4}=10^{1.6}\approx40$.
# Answer:
40