1. Measurement of Sound Decibel Notation Types of Sounds
Adding Sound Levels/Spectrum Level
Spectral Analysis
Shaping Spectra
Temporal Factors
Distortion

2. Decibel Notation Intensity is measured in Watts/cm2 Range of :
Just Audible W/cm2
to to
Just Painful W/cm2

3. 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”

4. SO, We need a simpler set of numbers
Something less unwieldy
The Solution is the BEL (after A.G. Bell)

5. The Genesis of the Bel the logarithm of the ratio of a measurement
to a reference value

6. 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

7. Inside the Logarithm is
A ratio of two numbers (or fraction)
An absolute measurement over
A reference value

8. The Reference Value for Intensity Level
is 1 x Watts/cm2
Bels IL = log ( Im/ 1 x W/cm2)
Where Im = measured intensity

9. The Range of Human Hearing
Detection
10-16 W/cm OR Bels
Pain
10-4 W/cm OR Bels

10. 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 W/cm2)

11. EXAMPLE:
What is IL of sound with absolute intensity of 2 x W/cm2
= 10 log (2 x W/cm2/1 x W/cm2)
= 10 log (2)
= 10 (0.3010)
= 3 dBIL

12. 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 ( )
= 6 dB

13. Bels or Decibels Can be calculated from any measure
But dB IL means something specific
Another scale is dB SPL
Sound Pressure Level

14. 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

15. 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

16. 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

17. SPL and IL Have EQUIVALENT reference values That is,
10-16W/cm2 of intensity produces
20 micropascals of pressure

18. Common Sound Measurements
Are made with a SOUND LEVEL METER
Which provides measure in dB SPL

19. 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

20. Periodic/Aperiodic Sounds
Periodic -- Repeating regular pattern with a constant period
Aperiodic-- no consistent pattern repeated.

21. 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

22. A Complex Sound

23. 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)

24. Waveform and Spectra

25. Harmonic Series When energy is present at multiples of some frequency
Lowest frequency = FUNDAMENTAL FREQ
Multiples of fundamental = HARMONICS

26. Not Everything is so Regular
Aperiodic sounds vary randomly
= NOISE
Waveforms may look wild
EXAMPLE:
White Gaussian Noise = equal energy at all frequencies

27. Gaussian Noise Waveform

28. Amp. Spectra: White & Pink Noise

29. Filters Shape Spectra
Attenuating (reducing) amplitudes in certain frequency ranges
Come in different types:
High-Pass
Low-Pass
Band-Pass
Band Reject

30. All Filters have definable:
Cutoff Frequency: Where attenuation reaches 3 dB
Rolloff: Rate (in dB/Octave) at which attenuation increases

31. Low and High Pass Filters

32. Band Pass and Reject Filters

33. Example of a Filter’s Effect

34. 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

35. Overall Level Equals Spectrum Level Plus Bandwidth Level
SPL Ls
Lbw

36. 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 dB
50 dB = Ls

37. 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?

38. 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/ W/cm2
(-16) = Im
= Im
2 x = Intensity of two sources
New IL = 10 log (2 x /10-16 W/cm2)

39. Working it out (cont’d)
New IL = 10 log (2 x (-16) )
= 10 (6.3010)
= 10 log (2 x 10 6)
= 63 dB IL

40. How About a SHORT CUT? New IL = IL of OLD # + 10 log (new #/old #)=
= 63 dB IL

41. Envelope--The Outline of the Waveform

42. 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.

43. AM Tone: Waveform & Spectrum

44. 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.

45. 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

46. 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.

47. 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

48. Distortion: Broad definition = any alteration of a sound
Specific def. = Addition of energy at frequencies not in the original sound

49. 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.