Measurement of Sound
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Transcript of Measurement of Sound
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Measurement of Sound
• Decibel Notation• Types of Sounds• Adding Sound Levels/Spectrum Level• Spectral Analysis• Shaping Spectra• Temporal Factors• Distortion
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Decibel Notation
• Intensity is measured in Watts/cm2
• Range of :• Just Audible 10-16 W/cm2 • to to• Just Painful 10-4 W/cm2
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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”
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SO, We need a simpler set of numbers
• Something less unwieldy
• The Solution is the BEL (after A.G. Bell)
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The Genesis of the Bel
• the logarithm of the ratio of a measurement to a reference value
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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
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Inside the Logarithm is
• A ratio of two numbers (or fraction)
• An absolute measurement over
• A reference value
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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
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The Range of Human Hearing
• Detection• 10-16 W/cm2 OR 0 Bels
• Pain• 10-4 W/cm2 OR 12 Bels
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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)
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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
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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
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Bels or Decibels
• Can be calculated from any measure• But dB IL means something specific• Another scale is dB SPL• Sound Pressure Level
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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
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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
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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
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SPL and IL• Have EQUIVALENT reference
values• That is,• 10-16W/cm2 of intensity produces• 20 micropascals of pressure
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Common Sound Measurements
• Are made with a SOUND LEVEL METER• Which provides measure in dB SPL
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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
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Periodic/Aperiodic Sounds
• Periodic -- Repeating regular pattern with a constant period
• Aperiodic-- no consistent pattern repeated.
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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
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A Complex Sound
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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)
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Waveform and Spectra
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Harmonic Series
• When energy is present at multiples of some frequency
• Lowest frequency = FUNDAMENTAL FREQ
• Multiples of fundamental = HARMONICS
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Not Everything is so Regular
• Aperiodic sounds vary randomly• = NOISE• Waveforms may look wild• EXAMPLE:• White Gaussian Noise = equal energy at all
frequencies
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Gaussian Noise Waveform
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Amp. Spectra: White & Pink Noise
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Filters Shape Spectra
• Attenuating (reducing) amplitudes in certain frequency ranges
• Come in different types:• High-Pass• Low-Pass• Band-Pass• Band Reject
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All Filters have definable:
• Cutoff Frequency: Where attenuation reaches 3 dB
• Rolloff: Rate (in dB/Octave) at which attenuation increases
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Low and High Pass Filters
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Band Pass and Reject Filters
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Example of a Filter’s Effect
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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
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Overall Level Equals Spectrum Level Plus Bandwidth Level
Lbw
Ls
SPL
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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
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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?
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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)
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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
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How About a SHORT CUT?
• New IL = IL of OLD # + 10 log (new #/old #)• = 60 + 10 log (2/1)• = 60 + 3• = 63 dB IL
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Envelope--The Outline of the Waveform
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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.
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AM Tone: Waveform & Spectrum
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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.
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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
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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.
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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
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Distortion:
• Broad definition = any alteration of a sound• Specific def. = Addition of energy at
frequencies not in the original sound
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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.