measurement of sound decibel notation types of sounds adding sound levels/spectrum level spectral...
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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 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.
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