Measurement of Sound Decibel Notation Types of Sounds

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/cm 2 Range of : Just Audible 10 -16 W/cm 2 to to Just Painful 10 -4 W/cm 2

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: “ZZZZZZZ”

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 -16 10 2 Watts/cm • Bels IL = log ( Im/ 1 x 10 -16 W/cm 2) • Where Im = measured intensity

The Range of Human Hearing • Detection • 10 -16 W/cm 2 OR 0 Bels • Pain • 10 -4 W/cm 2 OR 12 Bels

The Bel Is Too Gross a Measure For Us • So, We work in TENTHS OF BELS • The DECIBEL (d. B) • d. B IL = 10 log ( Im/ 1 x 10 -16 W/cm 2)

EXAMPLE: • What is IL of sound with absolute intensity of 2 x 10 -16 W/cm 2 • • = 10 log (2 x 10 -16 W/cm 2/1 x 10 -16 W/cm 2) = 10 log (2) = 10 (0. 3010) = 3 d. BIL

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 dist 2 /new dist 2 • = 1/4 or 0. 25 • d. B IL = 10 log (0. 25) = 10 (-0. 5991) = 6 d. B

Bels or Decibels • • Can be calculated from any measure But d. B IL means something specific Another scale is d. B 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 d. B SPL Equation • • • d. B IL = 10 log ( Im/ Iref) d. B SPL = 10 log ( Pm 2/ Pref 2) d. B SPL = 10 x 2 log (Pm/Pref) d. B SPL = 20 log (Pm/Pref) Reference Press. = 20 micropascals

SPL and IL • Have EQUIVALENT reference values • That is, • 10 -16 W/cm 2 of intensity produces • 20 micropascals of pressure

Common Sound Measurements • Are made with a SOUND LEVEL METER • Which provides measure in d. B 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 Reject

All Filters have definable: • Cutoff Frequency: Where attenuation reaches 3 d. B • Rolloff: Rate (in d. B/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 d. B) 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 d. B • and Bandwidth = 1000 Hz • • Lbw = 10 log (1000 Hz / 1 Hz) = 30 d. B SPL = Ls + Lbw 80 d. B = Ls + 30 d. B 50 d. B = 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 d. B IL, what would two produce?

Working out the example: • • one produces 60 d. B IL 60 = 10 log (Im/10 -16 W/cm 2) 6 = log (Im/10 -16 W/cm 2) 106 = Im/ 10 -16 W/cm 2 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/cm 2)

Working it out (cont’d) • New IL = 10 log (2 x 10 - (-16) ) • = 10 (6. 3010) • = 10 log (2 x 10 6) • = 63 d. B IL

How About a SHORT CUT? • New IL = IL of OLD # + 10 log (new #/old #) • = 60 + 10 log (2/1) • = 60 + 3 • = 63 d. B 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 peakclipping occurs • Intermodulation Distortion = production of energy at frequencies which are sums and/or differences of the input frequencies.