Statement I: A 80 dB sound has twice the intensity of a 40 dB sound.
Statement II: Loudness of a sound of a certain intensity I is defined as
`L("in "dB)=10log_(10)((I)/(I_0))`

Options

A. Statement I is true, Statement II is true: Statement II is a correct explanation for statement I.
B. Statement I is true, Statement II is true, Statement II is NOT a correct explanation for Statement I.
C. Statement I is true, Statement II is false
D. Statement I is falce: Statement II is true

Explanation

To solve the problem, we need to analyze both statements provided.

### Step-by-Step Solution:

**Step 1: Analyze Statement I**
- The statement claims that an 80 dB sound has twice the intensity of a 40 dB sound.
- To evaluate this, we use the formula relating sound levels in decibels (dB) to intensity:
\[ \beta = 10 \log_{10} \left( \frac{I}{I_0} \right) \]
where \( \beta \) is the sound level in dB, \( I \) is the intensity of the sound, and \( I_0 \) is the reference intensity (usually \( 10^{-12} \, \text{W/m}^2 \)).

**Step 2: Calculate the Intensities**
- Let \( \beta_1 = 40 \, \text{dB} \) and \( \beta_2 = 80 \, \text{dB} \).
- We can set up the equations for both sound levels:
\[ 40 = 10 \log_{10} \left( \frac{I_1}{I_0} \right) \]
\[ 80 = 10 \log_{10} \left( \frac{I_2}{I_0} \right) \]

**Step 3: Rearranging the Equations**
- From the first equation:
\[ \log_{10} \left( \frac{I_1}{I_0} \right) = 4 \implies \frac{I_1}{I_0} = 10^4 \implies I_1 = 10^4 I_0 \]
- From the second equation:
\[ \log_{10} \left( \frac{I_2}{I_0} \right) = 8 \implies \frac{I_2}{I_0} = 10^8 \implies I_2 = 10^8 I_0 \]

**Step 4: Compare Intensities**
- Now we can find the ratio of the intensities:
\[ \frac{I_2}{I_1} = \frac{10^8 I_0}{10^4 I_0} = 10^{8-4} = 10^4 \]
- This shows that \( I_2 \) (80 dB) is actually \( 10^4 \) times more intense than \( I_1 \) (40 dB), not twice as intense.

**Conclusion for Statement I:**
- Therefore, Statement I is **false**.

**Step 5: Analyze Statement II**
- Statement II states that loudness of a sound of a certain intensity \( I \) is defined as:
\[ L(\text{in dB}) = 10 \log_{10} \left( \frac{I}{I_0} \right) \]
- This is indeed the correct formula for calculating the sound level in decibels.

**Conclusion for Statement II:**
- Therefore, Statement II is **true**.

### Final Answer:
- Statement I is false, and Statement II is true.