Sound Pressure Level Calculator

What is Sound Pressure Level?

Sound Pressure Level (SPL) is a logarithmic measure of the effective pressure of a sound relative to a reference value. It quantifies the amplitude of sound waves in air or other media. SPL is commonly used to measure noise levels, audio equipment performance, and in various acoustic applications.

Formula

The formula for Sound Pressure Level is:

\[ SPL = 20 \log_{10}\left(\frac{P}{P_0}\right) \text{ dB} \]

Where:

• \( SPL \) is the Sound Pressure Level in decibels (dB)
• \( P \) is the measured root-mean-square (RMS) sound pressure in pascals (Pa)
• \( P_0 \) is the reference sound pressure, typically 20 μPa in air

Calculation Steps

Let's calculate the Sound Pressure Level for a given sound pressure:

1. Given:
   • Measured sound pressure (\( P \)) = 0.632 Pa
   • Reference sound pressure (\( P_0 \)) = 20 μPa = 0.00002 Pa
2. Apply the SPL formula: \[ SPL = 20 \log_{10}\left(\frac{P}{P_0}\right) \]
3. Substitute the known values: \[ SPL = 20 \log_{10}\left(\frac{0.632}{0.00002}\right) \]
4. Calculate the ratio inside the logarithm: \[ SPL = 20 \log_{10}(31600) \]
5. Compute the logarithm and multiply by 20: \[ SPL = 20 \times 4.4997 \approx 90 \text{ dB} \]

Example and Visual Representation

Let's visualize the concept of Sound Pressure Level:

This diagram illustrates:

• The logarithmic relationship between sound pressure ratio (P/P₀) and SPL
• The example point (green) showing 90 dB corresponding to a pressure ratio of 31600
• The curved red line representing the SPL formula