Measurement of Sound Decibel Notation Types of Sounds Adding Sound Levels/Spectrum Level Spectral Analysis Shaping Spectra Temporal Factors Distortion

Decibel Notation Intensity is measured in Watts/cm2 Range of : Just Audible 10-16 W/cm2 to to Just Painful 10-4 W/cm2

Can 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 value

What 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 logs

Inside the Logarithm is A ratio of two numbers (or fraction) An absolute measurement over A reference value

The 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 intensity

The Range of Human Hearing Detection 10-16 W/cm2 OR 0 Bels Pain 10-4 W/cm2 OR 12 Bels

The 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 dBIL

Example--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 dB

Bels or Decibels Can be calculated from any measure But dB IL means something specific Another scale is dB SPL Sound Pressure Level

Sound 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 2

Intensity = 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 Intensity

Deriving 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 micropascals

SPL and IL Have EQUIVALENT reference values That is, 10-16W/cm2 of intensity produces 20 micropascals of pressure

Common Sound Measurements Are made with a SOUND LEVEL METER Which provides measure in dB SPL

Types of Sounds So far we’ve talked a lot about sine waves periodic energy at one frequency But, not all sounds are like that

Periodic/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 aperiodic

A Complex Sound

Looking 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 Spectra

Harmonic Series When energy is present at multiples of some frequency Lowest frequency = FUNDAMENTAL FREQ Multiples of fundamental = HARMONICS

Not Everything is so Regular Aperiodic sounds vary randomly = NOISE Waveforms may look wild EXAMPLE: White Gaussian Noise = equal energy at all frequencies

Gaussian Noise Waveform

Amp. Spectra: White & Pink Noise

Filters Shape Spectra Attenuating (reducing) amplitudes in certain frequency ranges Come in different types: High-Pass Low-Pass Band-Pass Band Reject

All Filters have definable: Cutoff Frequency: Where attenuation reaches 3 dB Rolloff: Rate (in dB/Octave) at which attenuation increases

Low and High Pass Filters

Band Pass and Reject Filters

Example of a Filter’s Effect

Levels 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 + Lbw

Overall Level Equals Spectrum Level Plus Bandwidth Level SPL Ls Lbw

Example 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 = Ls

Combining 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 (cont’d) New IL = 10 log (2 x 10 -10 - (-16) ) = 10 (6.3010) = 10 log (2 x 10 6) = 63 dB IL

How About a SHORT CUT? New IL = IL of OLD # + 10 log (new #/old #) = 60 + 3 = 63 dB IL

Envelope--The Outline of the Waveform

One Interesting Envelope Amplitude Modulated Tone Tone whose energy is varied is called CARRIER You can also talk about the FREQUENCY OF MODULATION--How many times a second does amplitude cycle up and down and back again.

AM Tone: Waveform & Spectrum

Spectrum of an AM tone: Has Energy at 3 frequencies: 1. at the frequency of the CARRIER 2. at Carrier freq PLUS Modulation freq. 3. at Carrier freq MINUS Modulation freq.

Gating: Turning Sounds On and Off A tone on continuously theoretically has energy at only one frequency Turning a tone on and off will distort it and produce energy at other frequencies

Gating Terms: Onset--When amplitude begins to grow from zero. Rise Time -- Time taken for amplitude to go from zero to largest value. Offset--When peak amplitude begins to decrease from largest value. Fall Time -- Time taken for peak amplitude to go from largest value to zero.

Gating Effects--Spectral Splatter The Shorter the Rise/Fall Times, the greater the spread of energy to other frequencies. The Longer the Rise/Fall Times, the lesser the spread of energy. Overall (or Effective) Duration also controls spectral splatter

Distortion: Broad definition = any alteration of a sound Specific def. = Addition of energy at frequencies not in the original sound

Examples of Distortion: Harmonic Distortion = adding energy at multiples of input--often seen when peak-clipping occurs Intermodulation Distortion = production of energy at frequencies which are sums and/or differences of the input frequencies.