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

Lbw

Ls

SPL

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 + 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 CARRIER2. 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.