Sound Intensity Level Calculator

Understanding Sound Intensity Level Calculator

Sound intensity level uses the decibel scale. 0 dB is the threshold of hearing, 120 dB is the threshold of pain, 194 dB is the theoretical maximum.

How to use this calculator

1. Enter the sound intensity, \(I\), in watts per square meter.
2. Use the default reference intensity, \(I_0 = 1\times 10^{-12}\), unless your problem gives a different value.
3. Click calculate to get the sound intensity level, \(L\), in decibels.
4. Check the result and compare it with known sound levels, like a whisper or traffic.

The formula explained

The formula \(L = 10\log_{10}\frac{I}{I_0}\) computes the sound intensity level by comparing a sound's intensity to a reference intensity. It converts a ratio into decibels, which makes very large and very small intensities easier to work with.

• L = sound intensity level in decibels, \(\mathrm{dB}\)
• I = sound intensity in watts per square meter, \(\mathrm{W/m^2}\)
• \(I_0\) = reference intensity, usually \(1\times 10^{-12}\,\mathrm{W/m^2}\)
• \(\log_{10}\) = base-10 logarithm

Step by step method

1. Find the ratio \(\frac{I}{I_0}\).
2. Take the base-10 logarithm of that ratio.
3. Multiply the result by \(10\) to get \(L\) in decibels.

Worked example

Problem. Find the sound intensity level for \(I = 1\times 10^{-6}\,\mathrm{W/m^2}\) when \(I_0 = 1\times 10^{-12}\,\mathrm{W/m^2}\).

1. Compute the ratio, \(\frac{I}{I_0} = \frac{1\times 10^{-6}}{1\times 10^{-12}} = 10^6\).
2. Take the logarithm, \(\log_{10}(10^6) = 6\).
3. Multiply by \(10\), so \(L = 10\times 6 = 60\).

Tips and common mistakes

• Be sure \(I\) and \(I_0\) use the same units, usually \(\mathrm{W/m^2}\).
• If the intensity gets smaller than the reference intensity, the decibel value can be negative.

Frequently asked questions