This outline summarizes major points covered in lecture. It is not intended to replace your own lecture notes.
Instantaneous pressure p(t)
Proportional to velocity of system; sound pressure is proportional to air particle velocity
p(t) = (m v) / (t area), where m=mass, v=velocity, t=time
Sound pressure and energy
Energy—ability to do work, flows through medium
Power—rate of energy transfer through medium, rate at which work is accomplished
Power = Work/Time
Sound Energy—energy unit = Joule (J) = 1 N·m
Sound Power (W)—energy unit = Watt (W) = 1W = 1 J/s = 1 N·m/s
Note: sound energy and sound power are proportional but are not equivalent to each other
2 2 2
Sound Intensity ()—energy unit = Watt/m (W/m ) = 1 J/s·m
Sound intensity—amount of energy that is transmitted per second through an area of one square meter
Energy flowing through a volume
Acoustical energy from point source in expanding spherical wave front
Absolute vs relative measures
Power, intensity, pressure are absolute measures
Relative measures used as a reference for stating relative magnitude
Relative acoustic measures employ levels
Levels = ratio of absolute sound energy
Level expressed as a ratio, e.g. Power incidentower reference
Need to know the reference or standard in order for a level measure to be useful
bel
Number of bels calculated as: N(bels) = log (l10el); e.g. N(bels) = log (10 x ref
Bels: a relative measure without units
Advantage: provides a smaller range of values due to compressed scale with log system
Disadvantage: fractions commonly arise when dealing with smaller range
Solution: use decibels, calculated as: N(dB) = 10·N(bels); e.g. dB = 10·log ( / )
10 x ref
Intensity vs Pressure
Sound pressure (P)2is a scalar quantity; sound intensity () is a vector quantity
Equation: = [ P rms/(ρ·c) ], where ρ = density of medium and c = speed of sound in medium
Equation: Z =cρ·c = characteristic impedance of medium
Decibels and pressure
2
Standard dB equation cannot be used with sound pressure because P rms
dB = 10·log ( / ) used for calculating decibels using absolute intensity or power
10 x ref
dB = 20·log (10/Px) refsed for calculating decibels pressure
ISO standard for P ref= 20 µPa
When using the acronym dB SPL (SPL = sound pressure level) this implies P ref= 20 µPa
Usefulness of dB scale
large dynamic range from threshold of hearing to threshold of pain or even hearing damage
dynamic range can be as large 10 12 or 1014
possible to have negative dBs; it just means that the numerator is smaller than the denominator
Remember: once calculated, a dB is a dB is a dB
Standard dB reference
dB SPL—sound pressure level, re 20 µPa
-12 2
dB IL—intensity level, re 10 W/m
dB SL—sensation level, re some other measure, e.g., individual threshold
dB HL—hearing level, re level above average threshold of hearing at that frequency
Psych 3A03 14 September 2012
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