Find the sound level in decibels of a sound wave which has a intensity of `10^(-6) Wm^(-2)" , if I"_(0)= 10^(-12) Wm^(-2)`.

Answer

To find the sound level in decibels (dB) of a sound wave with a given intensity, we can use the formula:

\[ L = 10 \log_{10} \left( \frac{I}{I_0} \right) \]

where:
- \( L \) is the sound level in decibels,
- \( I \) is the intensity of the sound wave,
- \( I_0 \) is the reference intensity, typically \( 10^{-12} \, \text{W/m}^2 \).

### Step-by-Step Solution:

1. **Identify the given values**:
- \( I = 10^{-6} \, \text{W/m}^2 \)
- \( I_0 = 10^{-12} \, \text{W/m}^2 \)

2. **Substitute the values into the formula**:
\[ L = 10 \log_{10} \left( \frac{10^{-6}}{10^{-12}} \right) \]

3. **Simplify the fraction inside the logarithm**:
\[ \frac{10^{-6}}{10^{-12}} = 10^{-6 - (-12)} = 10^{-6 + 12} = 10^{6} \]

4. **Now substitute back into the formula**:
\[ L = 10 \log_{10} (10^{6}) \]

5. **Use the property of logarithms**:
\[ \log_{10} (10^{6}) = 6 \]

6. **Calculate the sound level**:
\[ L = 10 \times 6 = 60 \, \text{dB} \]

### Final Answer:
The sound level in decibels is \( 60 \, \text{dB} \).