• Logarithm Review
• Sound Pressure Level
• Sound Power
• Sound Intensity
• Multiple Sources

Sound Pressure, Intensity, and Power

The concepts of sound pressure, intensity, and power are easily confused. Sound pressure can be measured directly. Sound intensity and power are related to pressure but have important distinctions.

Logarithm Review

• $y = 10^{x}$: $x = \log_{10}(y)$

• $\log A B = \log A + \log B$

• $\log A/B = \log A - \log B$

• $\log A^{n} = n \log A$

Sound Pressure Level

• ``Threshold of audibility'' or the minimum pressure fluctuation detected by the ear is less than $10^{-9}$ of atmospheric pressure or about $2 \times 10^{-5}$ N/m$^{2}$ at 1000 Hz.

• ``Threshold of pain'' corresponds to a pressure $10^{6}$ times greater than the audibility threshold, but still less than 1/1000 of atmospheric pressure.

• Because the ear is sensitive to such a wide range of pressure variations, sound pressure measurements are made on a logarithmic scale (decibel scale).

• Sound Pressure Level (SPL) $= 20 \log (p / p_{0}) = 10 \log (p / p_{0})^{2}$, where $p_{0} = 2 \times 10^{-5}$ N/m$^{2}$.

• SPL is proportional to the average squared pressure amplitude.

• ``Threshold of audibility'': 0 dB SPL; ``Threshold of Pain'': 120 dB SPL

• In a free field, pressure varies as $1 / r$ for an omni-directional source. This corresponds to a 6 dB decrease in SPL for each doubling of distance from the source.

Sound Power

• Total sound power emitted by a source in all directions.

• Measured in watts (joules / second).

• Sound Power Level (PWL) = $10 \log (W / W_{0})$, where $W_{0} = 10^{-12}$ watts.

• Indicates the strength of a sound source, irrespective of the location of source and observer.

Sound Intensity

• Rate of energy flow across a unit area (power per unit area).

• Sound Intensity Level (IL) = $10 \log (I / I_{0})$, where $I_{0} = 10^{-12}$ watts/meter$^{2}$.

• In a free field, intensity varies as $1 / r^{2}$ for an omni-directional source. This corresponds to a 6 dB decrease in intensity for each doubling of distance from the source.

• In a free field, IL and SPL are nearly equal for a single source.

Multiple Sources

• Two equal sources produce a 3 dB increase in sound power level.

• Two equal sources produce a 3 dB increase in sound pressure level, assuming no interference.

• Two 80 dB sources add to produce an 83 dB SPL.