Measurement of Sound

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 10-16 W/cm2 • to to • Just Painful 10-4 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 10-16 Watts/cm2 • Bels IL = log ( Im/ 1 x 10-16 W/cm2) • Where Im = measured intensity

9. The Range of Human Hearing • Detection • 10-16 W/cm2 OR 0 Bels • Pain • 10-4 W/cm2 OR 12 Bels

10. The Bel Is Too Gross a Measure For Us • So, We work in TENTHS OF BELS • The DECIBEL (dB) • dB IL = 10log ( Im/ 1 x 10-16 W/cm2)

11. 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

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 (-0.5991) = 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 = 10log ( Im/ Iref) • dB SPL = 10log ( 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 + 30 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/ 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)

39. 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

40. How About a SHORT CUT? • New IL = IL of OLD # + 10 log (new #/old #) • = 60 + 10 log (2/1) • = 60 + 3 • = 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.