To compute the intensity level (IL) in decibels (dB), we use the formula:

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

Where:
- \( I \) is the intensity of the sound in \( \text{W/m}^2 \).
- \( I_0 \) is the reference intensity, typically \( 1 \times 10^{-12} \, \text{W/m}^2 \), which corresponds to the threshold of hearing.

Given:
- \( I = 10^{-13} \, \text{W/m}^2 \)
- \( I_0 = 1 \times 10^{-12} \, \text{W/m}^2 \)

Now, let's compute the intensity level.

\[
IL = 10 \cdot \log_{10}\left(\frac{10^{-13}}{10^{-12}}\right) = 10 \cdot \log_{10}\left(10^{-1}\right)
\]

\[
IL = 10 \cdot (-1) = -10 \, \text{dB}
\]

The intensity level is **-10 dB**.

Would you like further details or clarification on any part of the calculation? Here are some related questions:

1. How is sound intensity measured in practice?
2. What is the reference level for sound intensity in decibels?
3. What happens when the intensity is lower than the reference \( I_0 \)?
4. Can you explain the relationship between intensity and loudness perception?
5. How does distance affect the intensity level of a sound?

**Tip:** The decibel scale is logarithmic, meaning each increase of 10 dB represents a tenfold increase in sound intensity.

Learn how to compute the sound intensity level (IL) in decibels for a sound intensity of 10^-13 W/m^2. Using the logarithmic formula IL = 10 * log10(I / I_0), we calculate the intensity level as -10 dB. This solution is suitable for high school students learning about sound physics and logarithmic calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation