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:

“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 10 1 = 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/cm 2 • 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 (dB) • dB 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 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 dist 2 /new dist 2 • = 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/ I ref ) • dB SPL = 10 log ( Pm 2 / P ref 2 ) • dB SPL = 10 x 2 log (Pm/P ref ) • dB SPL = 20 log (Pm/P ref ) • 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 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:

reaches 3 dB Where attenuation •

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 Ls SPL 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/cm 2 ) • 6 = log (Im/10 -16 W/cm 2 ) • 10 6 = 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 -10 - (-16) ) = 10 (6.3010) = 10 log (2 x 10 = 63 dB IL 6 )

How About a SHORT CUT?

• • • • New IL = IL of OLD # + 10 log (new # / old #) = 60 + 10 log (2/1) = 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.