Sound Intensity Level Calculator

What is Sound Intensity Level?

Sound Intensity Level (SIL) is a logarithmic measure of the sound intensity in a specified direction relative to a reference value. It quantifies the amount of sound energy flowing through a unit area per unit time. SIL is commonly used in acoustics to describe the loudness of sounds and to assess noise levels in various environments.

Formula

The formula for Sound Intensity Level is:

\[ SIL = 10 \log_{10}\left(\frac{I}{I_0}\right) \text{ dB} \]

Where:

• \( SIL \) is the Sound Intensity Level in decibels (dB)
• \( I \) is the measured sound intensity in watts per square meter (W/m²)
• \( I_0 \) is the reference sound intensity, typically 10⁻¹² W/m²

Calculation Steps

Let's calculate the Sound Intensity Level for a given sound intensity:

1. Given:
   • Measured sound intensity (\( I \)) = 10⁻⁶ W/m²
   • Reference sound intensity (\( I_0 \)) = 10⁻¹² W/m²
2. Apply the SIL formula: \[ SIL = 10 \log_{10}\left(\frac{I}{I_0}\right) \]
3. Substitute the known values: \[ SIL = 10 \log_{10}\left(\frac{10^{-6}}{10^{-12}}\right) \]
4. Simplify the fraction inside the logarithm: \[ SIL = 10 \log_{10}(10^6) \]
5. Compute the logarithm and multiply by 10: \[ SIL = 10 \times 6 = 60 \text{ dB} \]

Example and Visual Representation

Let's visualize the concept of Sound Intensity Level:

This diagram illustrates:

• The logarithmic relationship between sound intensity ratio (I/I₀) and SIL
• The example point (green) showing 60 dB corresponding to an intensity ratio of 10⁶
• The curved red line representing the SIL formula