It looks like your statement about sound intensity was cut off. However, I believe you're referring to the threshold of hearing, where the minimum intensity of sound the human ear can detect is $I_0 = 10^{-12} \, \text{W/m}^2$.

This intensity corresponds to 0 decibels (dB) on the decibel scale, which measures the loudness of sound based on the logarithmic scale. The formula for calculating the sound level in decibels is given by:

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

Where:

• $L$ is the sound level in decibels (dB),
• $I$ is the intensity of the sound (in watts per square meter, W/m²),
• $I_0$ is the reference intensity, typically $I_0 = 10^{-12} \, \text{W/m}^2$ (the threshold of hearing).

If $I = I_0$, then:

$L = 10 \log_{10} \left( \frac{I_0}{I_0} \right) = 10 \log_{10}(1) = 0 \, \text{dB}$

Thus, the minimum detectable sound intensity, $I_0$, is defined as 0 dB.

Would you like more details or further explanation? Here are some related questions for practice:

1. How do you calculate the sound level for a sound with an intensity of $10^{-8} \, \text{W/m}^2$?
2. What is the relationship between intensity and decibels in a noisier environment?
3. If a sound measures 30 dB, what is its intensity in $\text{W/m}^2$?
4. How does the human ear perceive differences in decibels?
5. What is the typical sound intensity of normal conversation in $\text{W/m}^2$?

Tip: The decibel scale is logarithmic, meaning that a small change in dB corresponds to a large change in actual sound intensity.