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]
    • velocity [m/s]
    • acceleration [m/s²]
    • pressure [Pa]
    • density [kg/m³]
  • 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 time-averaged power density of a wave at a particular location.
  • The SI unit of intensity is the watt per square meter.
  • As an equation, intensity is defined as…

    I =	⟨P⟩
    	A

    Where…

    I =	intensity
    ⟨P⟩ =	time-averaged power
    A =	area through which the wave is propagating in a plane perpendicular to the direction of propagation

  • When the amplitude of a sound wave is measured by the maximum displacement of the particles that make up the medium, its intensity is equal to…

    I = 2π²ρf²v∆s²

    Where…

    I =	intensity
    ∆s =	maximum displacement of particles in the medium (displacement amplitude)
    ρ =	density of medium
    f =	wave frequency
    v =	wave speed

  • When the amplitude of a sound wave is measured by the maximum gauge pressure of the medium in bulk, its intensity is equal to…

    I =	∆P2
    	2ρv

    Where…

    I =	intensity
    ∆P =	maximum gauge pressure (pressure amplitude)
    ρ =	density of medium
    v =	wave speed

  • When the amplitude of a sound wave is measured by the maximum change in density of the medium in bulk, its intensity is equal to…

    I =	∆ρ2v3
    	2ρ

    Where…

    I =	wave intensity
    Δρ =	maximum density change (density amplitude)
    ρ =	density of medium
    v =	wave speed

• The level (L) of a quantity is the logarithm of the quantity compared to a reference value for the quantity.
  • When the logarithm used is base ten, the SI unit is the bel (B).
    • Although the bel is computed from quantities with units, the bel is itself unitless.
    • The bel is too big for most purposes so the decibel (dB) is more common.

      1 bel = 10 decibel

    • A level increase of 3 dB is approximately equal to a doubling of intensity (since log 2 ≈ 0.3).
  • Sound level values are typically computed using intensity or pressure amplitude.
    • The equation for sound intensity level (often abbreviated SIL) in decibels is…

      LI = 10 log	⎛ ⎜ ⎝	I	⎞ ⎟ ⎠
      		I0

      where…

      LI =	sound intensity level [dB]
      I =	intensity [W/m2]
      I0 =	reference intensity [W/m2]

    • The equation for sound pressure level (often abbreviated SPL) in decibels is…

      LP = 20 log	⎛ ⎜ ⎝	∆P	⎞ ⎟ ⎠
      		∆P0

      where…

      LP =	sound pressure level [dB]
      ∆P =	maximum gauge pressure or pressure amplitude [W/m2]
      ∆P0 =	reference gauge pressure [W/m2]

    • The standard reference values for sounds are defined from pressure amplitudes.
      • By definition, a pressure amplitude of 20 μPa in air corresponds to a sound pressure level of 0 dB.
      • By definition, a pressure amplitude of 1 μPa in water corresponds to a sound pressure level of 0 dB.
  • Levels are also commonly used for quantities in audio electronics, radio transmission, and other branches of science and engineering.
• Loudness is…
  • FINISH THIS!