Auditory Theory: Acoustics

Lecture 003 Sound II

Reading Assignment for Lecture 004

Before next class please read Section

• 1.5.n Sound Interactions

Pages 33 to 51 of Acoustics and Psychoacoustics. We may have a brief quiz on this section at the beginning of the next class.

Brain Bullets

• Logarithms
  • 1.3 = 10^a - a is called the logarithm of 1.3
  • Can multiply by adding
  • Form a compressed scale

• Joules
  • a measure of the total sound energy present
  • Symbol: J
  • Units: Kilogram square meters per second per second (Kg m²s^-2)

• Watts
  • the rate of energy released over time
  • Symbol: W
  • Units: Joules/second (Js^-1 )

• Decibel
  • The dB is a logarithmic unit used to describe a ratio. The ratio may be power, sound pressure, voltage or intensity or several other things.
  • Symbol: dB
  • Units: It is a log of a ratio

• Sound Power Level (SWL)
  • Measure of the total power of a sound
  • Ratio between measured power and reference power
  • SWL = 10 log₁₀(W_actual/ W_reference ) where W_reference=10^-12 Watts (1 pico watt)
  • Symbol: dB(SWL)
  • Units: dB_SWL

• Sound Intensity Level (SIL)
  • A measure of power through an area
  • ratio between measured intensity and reference intensity
  • 10 log₁₀(I_actual / I_reference ) where I_reference = 10^-12 Watts m^-2 (1 pico watt per square meter)
  • Symbol: dB(SIL)
  • Units: dB_SIL

• Sound Pressure Level
  • ratio between measured pressure level and reference power (threshold of hearing)
  • SPL = 20 log₁₀ (P_actual/P_reference) where P_reference= 20 μPa or 20 x l0^-6 Pa
  • Symbol: SPL
  • Units: dB_SPL

• Adding sounds together
  • Correlated -The sound comes from several sources which are related.
    • Multiple sources of the same sound (a mono signal in two speakers).
    • Short reflections and multiple sources can generate correlated sources
  • Uncorrelated - the sounds come from unrelated sources.
    • instruments in an ensemble playing different pitches.
    • the same source but one has been delayed so much as to no longer be correlated

• Phase alignment
  • When correlated sounds are added the result depends on their phase alignment.
  • Sounds which are aligned will add
  • Sounds which are not aligned will cancel each other out at 180°
  • At other angles they will combine destructively to some degree.

• When uncorrelated sounds add
  • Adding uncorrelated sounds of equal volume you get a 3 db increase for every source you add.
  • Adding uncorrelated sounds of unequal volume dB have to be converted back to ratios before they are added together. This is because adding lags is actually multiplying

• Inverse square Law
  • Describes the reduction of sound intensity with distance
  • Intensity = Powersource /4π r2
  • Double the distance cuts the intensity by four

• Boundaries
  • Adding boundaries increases the gain from a speaker by 3 dB for each boundary added