The Physics
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Opus in profectus

# Intensity

## Summary

• Amplitude, intensity, and loudness are often used interchangeably, but the three terms have different meanings.
• Amplitude is a measure of the maximal change in whatever quantity is varying in a wave.
• For sound waves, the varying quantity [and its SI unit] could be…
• position [m],
• density [kg/m3], or
• pressure [Pa].
• Position and density variations caused by sound waves are difficult to measure directly since…
• their magnitudes are small and
• the period of sound waves are brief.
• Pressure variations caused by sound waves can be detected…
• by animals with their ears and
• by machines with microphones
• Intensity is an objective measure of the mean power density of the energy transferred by a wave.
• The SI unit of intensity is the watt per square meter.
• As an equation, intensity is defined as…  I = ⟨P⟩ A

where…

 I = intensity of wave ⟨P⟩ = time-averaged transmitted power A = area through which the wave or a portion of the wave is propagating
• When amplitude is measured by maximum displacement, intensity is equal to…  I = 2π2ρƒ2vΔx2max

where…

 I = intensity of wave ρ = density of medium = frequency of wave v = speed of wave Δx2max = maximum displacement of particles in the medium
• When amplitude is measured by maximum gauge pressure, intensity is equal to…  I = P2 2ρv

where…

 I = intensity of wave P = maximum gauge pressure ρ = density of medium v = speed of wave