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.

As an equation, intensity is defined as …

where …

I	intensity of the 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 = 2π²ρf²vΔx²_max

where …

I	intensity of the wave
ρ	density of the medium
f	frequency of the wave
v	speed of the wave
Δx²_max	maximum displacement of the particles in the medium

When amplitude is measured by maximum gauge pressure, intensity is equal to …

where …