Measurement of SoundDecibel NotationCan You Imagine?SO, We need a simpler set of numbersThe Genesis of the BelWhat is a log?Inside the Logarithm isThe Reference Value for Intensity LevelThe Range of Human HearingThe Bel Is Too Gross a Measure For UsEXAMPLE:Example--Relative ChangeBels or DecibelsSound Pressure and Sound IntensityIntensity = Pressure SquaredDeriving the dB SPL EquationSPL and ILCommon Sound MeasurementsTypes of SoundsPeriodic/Aperiodic SoundsSimple/Complex SoundsA Complex SoundLooking at a WaveformWaveform and SpectraHarmonic SeriesNot Everything is so RegularGaussian Noise WaveformAmp. Spectra: White & Pink NoiseFilters Shape SpectraAll Filters have definable:Low and High Pass FiltersBand Pass and Reject FiltersExample of a Filter’s EffectLevels of a Band of NoiseOverall Level Equals Spectrum Level Plus Bandwidth LevelExample of Deriving LsCombining Sound SourcesWorking out the example:Working it out (cont’d)How About a SHORT CUT?Envelope--The Outline of the WaveformOne Interesting EnvelopeAM Tone: Waveform & SpectrumSpectrum of an AM tone:Gating: Turning Sounds On and OffGating Terms:Gating Effects--Spectral SplatterDistortion:Examples of Distortion:Measurement of Sound•Decibel Notation•Types of Sounds•Adding Sound Levels/Spectrum Level•Spectral Analysis•Shaping Spectra•Temporal Factors•DistortionDecibel Notation•Intensity is measured in Watts/cm2•Range of :•Just Audible 10-16 W/cm2 •to to•Just Painful 10-4 W/cm2Can You Imagine?•AUDIOLOGIST: “Mr. Smith, you hearing in the right ear is down to about 3 times ten to the negative twelfth Watts per square centimeter, while your left ear is a little bit better at ten to the negative fourteenth…”•MR. SMITH: “ZZZZZZZZZZZZZ”SO, We need a simpler set of numbers•Something less unwieldy•The Solution is the BEL (after A.G. Bell)The Genesis of the Bel•the logarithm of the ratio of a measurement to a reference valueWhat is a log?•Log (x) = power you would raise 10 to to get x•e.g., log (10) = 1• because 101 = 10•or, log (0.01) = -2• because 0.01 = 10-2•You can use a calculator to obtain logsInside the Logarithm is•A ratio of two numbers (or fraction)•An absolute measurement over•A reference valueThe Reference Value for Intensity Level•is 1 x 10-16 Watts/cm2•Bels IL = log ( Im/ 1 x 10-16 W/cm2)•Where Im = measured intensityThe Range of Human Hearing•Detection•10-16 W/cm2 OR 0 Bels•Pain•10-4 W/cm2 OR 12 BelsThe Bel Is Too Gross a Measure For Us•So, We work in TENTHS OF BELS•The DECIBEL (dB)•dB IL = 10 log ( Im/ 1 x 10-16 W/cm2)EXAMPLE:•What is IL of sound with absolute intensity of 2 x 10-16 W/cm2•= 10 log (2 x 10-16 W/cm2/1 x 10-16 W/cm2)•= 10 log (2)•= 10 (0.3010)•= 3 dBILExample--Relative Change•How will the intensity level change if you move to twice as far from a source?•We know that intensity change = old dist2 /new dist2• = 1/4 or 0.25•dB IL = 10 log (0.25) = 10 (-0.5991) = 6 dBBels or Decibels•Can be calculated from any measure•But dB IL means something specific•Another scale is dB SPL•Sound Pressure LevelSound Pressure and Sound Intensity•Are not the same thing•Pressure = Force per unit Area (earlier called “stress”)•Sound Pressure is force exerted by sound in a given area•Intensity also involves 1/area•But, Intensity = Pressure 2Intensity = Pressure Squared•Anything that doubles intensity will raise pressure by only the square root of two.•Any change in pressure is accompanied by that change squared in intensity•Doubling Pressure = Quadrupling IntensityDeriving the dB SPL Equation•dB IL = 10 log ( Im/ Iref)•dB SPL = 10 log ( Pm2/ Pref2)•dB SPL = 10 x 2 log (Pm/Pref)•dB SPL = 20 log (Pm/Pref)•Reference Press. = 20 micropascalsSPL and IL•Have EQUIVALENT reference values•That is,•10-16W/cm2 of intensity produces•20 micropascals of pressureCommon Sound Measurements•Are made with a SOUND LEVEL METER•Which provides measure in dB SPLTypes of Sounds•So far we’ve talked a lot about sine waves•periodic•energy at one frequency•But, not all sounds are like thatPeriodic/Aperiodic Sounds•Periodic -- Repeating regular pattern with a constant period•Aperiodic-- no consistent pattern repeated.Simple/Complex Sounds•Simple -- Having energy at only one frequency• have a sinusoidal waveform•Complex -- Having energy at more than one frequency• may be periodic or aperiodicA Complex SoundLooking at a Waveform•You may not be able to tell much about frequencies present in the sound•Another way of displaying sound energy is more valuable:AMPLITUDE SPECTRUM--display of amplitude (y-axis) as a function of frequency (x-axis)Waveform and SpectraHarmonic Series•When energy is present at multiples of some frequency•Lowest frequency = FUNDAMENTAL FREQ•Multiples of fundamental = HARMONICSNot Everything is so Regular•Aperiodic sounds vary randomly•= NOISE•Waveforms may look wild•EXAMPLE:•White Gaussian Noise = equal energy at all frequenciesGaussian Noise WaveformAmp. Spectra: White & Pink NoiseFilters Shape Spectra•Attenuating (reducing) amplitudes in certain frequency ranges•Come in different types:•High-Pass•Low-Pass•Band-Pass•Band RejectAll Filters have definable:•Cutoff Frequency: Where attenuation reaches 3 dB•Rolloff: Rate (in dB/Octave) at which attenuation increasesLow and High Pass FiltersBand Pass and Reject FiltersExample of a Filter’s EffectLevels of a Band of Noise•Overall Level = SPL (Total Power) •Spectrum Level = Ls level at one frequency•Bandwidth Level = Lbw freq width (in dB) Lbw = 10 log (bandwidth (in Hz)/ 1 Hz)•SPL = Ls + LbwOverall Level Equals Spectrum Level Plus Bandwidth LevelLbwLsSPLExample of Deriving Ls•Given SPL = 80 dB•and Bandwidth = 1000 Hz•Lbw = 10 log (1000Hz / 1Hz) = 30 dB•SPL = Ls + Lbw•80 dB = Ls + 30 dB•50 dB = LsCombining Sound Sources•Adding additional (identical) sources produces summing of intensities•e.g., adding a second speaker playing the same siganl•If one produced 60 dB IL, what would two produce?Working out the example:•one produces 60 dB IL•60 = 10 log (Im/10-16 W/cm2)•6 = log (Im/10-16 W/cm2)•106 = Im/ 10-16 W/cm2•10 6 + (-16) = Im•10 -10 = Im•2 x 10 -10 = Intensity of two sources•New IL = 10 log (2 x 10 -10 /10-16 W/cm2)Working it out