2. SPPA 6010 Advanced Speech Science 1 Topic 3 Physical Acoustics Review

3. WARNING!!!! This is a REVIEW. Mastery is ESSENTIAL to understand the material later in the course. If you found this material particularly challenging in previous courses it is, spend the time on it NOW. SPPA 6010 Advanced Speech Science 2

4. 3 Learning Objectives Outline the physical processes underlying simple harmonic motion using the mass- spring model Describe the molecular basis of sound wave propagation

5. SPPA 6010 Advanced Speech Science 4 Spring Mass Model Mass (inertia) Elasticity Friction

6. SPPA 6010 Advanced Speech Science 5 What is sound? It may be defined as the propagation of a pressure wave in space and time. propagates through a medium

7. SPPA 6010 Advanced Speech Science 6 Sound-conducting media Medium is composed of molecules Molecules have “wiggle room” Molecules exhibit random motion Molecules can exert pressure AB

8. SPPA 6010 Advanced Speech Science 7 Model of air molecule vibration (Time 1) Rest positions Air molecules sitting side by side

9. SPPA 6010 Advanced Speech Science 8 Model of air molecule vibration (Time 2)

10. SPPA 6010 Advanced Speech Science 9 Model of air molecule vibration (Time 3)

11. SPPA 6010 Advanced Speech Science 10 Model of air molecule vibration (Time 4)

12. SPPA 6010 Advanced Speech Science 11 Model of air molecule vibration (Time 5)

13. SPPA 6010 Advanced Speech Science 12 Model of air molecule vibration Time 1 2 3 4 5 Distance abcd

14. SPPA 6010 Advanced Speech Science 13 Wave action of molecular motion Time 1 2 3 4 5 Distance

15. SPPA 6010 Advanced Speech Science 14 Amplitude waveform Position Time

16. SPPA 6010 Advanced Speech Science 15 Amplitude waveform Amplitude Time Question: How long will this last?

17. SPPA 6010 Advanced Speech Science 16 Model of air molecule vibration Time 1 2 3 4 5 Pressure measuring device Questions: Where is a region of compression? Where is a region of rarefaction?

18. SPPA 6010 Advanced Speech Science 17 For example… Pressure Time

19. SPPA 6010 Advanced Speech Science 18 Learning Objectives Define the key characteristics of sinusoidal motion (amplitude, frequency/period and phase) Outline the relationship between the frequency and wavelength of a sound wave

20. SPPA 6010 Advanced Speech Science 19 Pressure vs. time (pressure waveform) Pressure Time Amplitude Period (T) Phase: when a period begins Frequency (F): rate that waveform repeats itself (1/T) Phase (deg)

21. SPPA 6010 Advanced Speech Science 20 Phase

22. SPPA 6010 Advanced Speech Science 21 Initiating a sound waves that differ only in phase A force is applied to molecule at frequency f and time t same force applied at frequency f at time t+a where a < the period of vibration

23. SPPA 6010 Advanced Speech Science 22 Features of a pressure waveform Amplitude –Measured in pressure units –peak amplitude –peak-to-peak amplitude –Instantaneous amplitude Period and Frequency –Period measured in time (basic quantity) –Frequency is a rate measure (per unit time) expressed as Hertz (s -1 ) –May be expressed as octaves, semitones, etc Phase –Measured in degrees (relative to period length) –0-360 degrees

24. SPPA 6010 Advanced Speech Science 23 Spatial variation in pressure wave wavelength ( ) is the distance covering adjacent high and low pressure regions

25. SPPA 6010 Advanced Speech Science 24 For example… Distance Wavelength ( ) Pressure

26. SPPA 6010 Advanced Speech Science 25 Relation between frequency and wavelength =c/F where : wavelength F: is the frequency c: is sound speed in medium (35,000 cm/sec)

27. SPPA 6010 Advanced Speech Science 26 Additional Concepts Propagation of waves –Transmission –Absorption –Reflection –Reverberation

28. SPPA 6010 Advanced Speech Science 27 Learning Objectives Draw and describe time-domain and frequency-domain representation of sound Distinguish between simple and complex sound sounds with regard to physical characteristics and graphical representations Distinguish between periodic and aperiodic sounds with specific emphasis on terms such as fundamental frequency/period, harmonics, and overtones Distinguish between continuous and transient sounds Describe how waves sum, define Fourier's theorem and be able to describe the basics of Fourier analysis

29. SPPA 6010 Advanced Speech Science 28 Graphic representation of sound Time domain –Called a waveform –Amplitude plotted as a function of time Frequency domain –Called a spectrum –Amplitude spectrum amplitude vs. frequency –Phase spectrum phase vs. frequency –May be measured using a variety of “window” sizes

30. SPPA 6010 Advanced Speech Science 29 Same sound, different graphs Time domain Frequency domain From Hillenbrand

31. SPPA 6010 Advanced Speech Science 30 Classification of sounds Number of frequency components –Simple –Complex Relationship of frequency components –Periodic –Aperiodic Duration –Continuous –Transient

32. SPPA 6010 Advanced Speech Science 31 Simple periodic sound Simple: one frequency component Periodic: repeating pattern Completely characterized by –amplitude –period (frequency) –phase Other names: sinusoid, simple harmonic motion, pure tone

33. SPPA 6010 Advanced Speech Science 32 Simple periodic sound: Graphic appearance From Hillenbrand

34. SPPA 6010 Advanced Speech Science 33 Complex periodic sounds Complex: > one frequency component Periodic: repeating pattern Continuous Frequencies components have a special relation –Lowest frequency: fundamental frequency Symbol: f o Frequency component with longest period –Higher frequency components: harmonics integer (whole number) multiples of the f o

35. SPPA 6010 Advanced Speech Science 34 Complex periodic sounds: Graphic appearance Time domain: –repeating pattern of pressure change –within the cycle, things look complex Frequency domain: –spectral peaks at evenly spaced frequency intervals –“picket fence” appearance Auditory impression: sounds ‘musical’

36. SPPA 6010 Advanced Speech Science 35 Complex periodic sounds: Graphic appearance From Hillenbrand

37. SPPA 6010 Advanced Speech Science 36

38. SPPA 6010 Advanced Speech Science 37 Amplitude vs. Phase Spectrum Amplitude spectrum: different Phase spectrum: same

39. SPPA 6010 Advanced Speech Science 38 Amplitude vs. Phase Spectrum Amplitude spectrum: same Phase spectrum: different

40. SPPA 6010 Advanced Speech Science 39 (Complex) Aperiodic sounds Complex: > one frequency component Aperiodic: Does not repeat itself Frequency components are not systematically related May be –Continuous –Transient

41. SPPA 6010 Advanced Speech Science 40 Aperiodic sounds: Graphic appearance Time domain: –no repeating pattern of pressure change Frequency domain: –the spectrum is dense –No “picket fence” Auditory impression: sounds ‘noisy’

42. SPPA 6010 Advanced Speech Science 41 Aperiodic sounds: Graphic appearance From Hillenbrand

43. SPPA 6010 Advanced Speech Science 42 Analysis of complex waves Waves can be summed Complex waves are the sum of simple waves Fourier: French Mathematician: –Any complex waveform may be formed by summing sinusoids of various frequency, amplitude and phase Fourier Analysis –Provides a unique (only one) solution for a given sound signal –Is reflected in the amplitude and phase spectrum of the signal –Reveals the building blocks of complex waves, which are sinusoids

44. SPPA 6010 Advanced Speech Science 43 Learning Objectives Draw and differentiate the waveform and the waveform envelope Draw and differentiate the amplitude spectrum, the phase spectrum and the spectrum envelope

45. SPPA 6010 Advanced Speech Science 44 The “envelope” of a sound wave Waveform envelope: –imaginary smooth line that follows the peak of the amplitude of a sound pressure waveform Spectrum envelope: –Imaginary smooth line drawn on top of the amplitude spectrum

46. SPPA 6010 Advanced Speech Science 45 Waveform envelope Time

47. SPPA 6010 Advanced Speech Science 46 Spectrum envelope From Hillenbrand

48. SPPA 6010 Advanced Speech Science 47 Thought Question Can an aperiodic and complex periodic sound have identical spectrum envelopes?

49. SPPA 6010 Advanced Speech Science 48 Amplitude Spectrum: Window Size “short-term” vs. “long-term average” amplitude spectrum

50. SPPA 6010 Advanced Speech Science 49 “Instantaneous” Amplitude Spectra

51. SPPA 6010 Advanced Speech Science 50 (Long Term) Average Amplitude Spectrum

52. SPPA 6010 Advanced Speech Science 51

53. SPPA 6010 Advanced Speech Science 52 Learning Objectives Define an acoustic filter Draw and label a frequency response curve Draw and differentiate different types of acoustic filters Define terms such as cutoff frequency, center frequency, roll off rate, gain, and bandwidth Define and draw a basic filter system and relate that to the source-filter theory of speech production

54. SPPA 6010 Advanced Speech Science 53 What is an “Acoustic” Filter holds back (attenuates) certain sounds and lets other sounds through - selective.

55. SPPA 6010 Advanced Speech Science 54 Why might we be interested in filters? Human vocal tract acts like a frequency selective acoustic filter Human auditory system behaves as a frequency selective filter helps us understand how speech is produced and perceived.

56. SPPA 6010 Advanced Speech Science 55 Frequency Response Curve (FRC) Frequency lowhigh Gain + - Center frequency lower cutoff frequency upper cutoff frequency passband 3 dB

57. SPPA 6010 Advanced Speech Science 56 Operation of a filter on a signal NOTE: Amplitude spectrum describes a sound Frequency response curve describes a filter

58. SPPA 6010 Advanced Speech Science 57 Kinds of frequency selective filters Low-pass filters –Lets low frequencies “pass through” and attenuates high frequencies High-pass filters –Lets high frequencies “pass through” and attenuates low frequencies Band-pass filters –Lets a particular frequency range “pass through” and attenuates other frequencies

59. SPPA 6010 Advanced Speech Science 58 Low Pass Filters Frequency lowhigh Gain + -

60. SPPA 6010 Advanced Speech Science 59 High Pass Filters Frequency lowhigh Gain + -

61. SPPA 6010 Advanced Speech Science 60 Band Pass Filter Frequency lowhigh Gain + -

62. SPPA 6010 Advanced Speech Science 61 Learning Objectives Define resonance, free and forced vibration Outline how acoustic resonators behave like acoustic filters

63. SPPA 6010 Advanced Speech Science 62 Free vibration objects tend to vibrate at a characteristic or resonant frequency (RF)

64. SPPA 6010 Advanced Speech Science 63 Forced vibration A vibrating system can force a nearby system into vibration The efficiency with which this is accomplished is related to the similarity in the resonant frequency (RF) of the two systems

65. SPPA 6010 Advanced Speech Science 64 Forced vibration If the RF of the two systems are the same, the amplitude of forced vibration will be large If the RF of the two systems are quite different, the amplitude of forced vibration will be small or nonexistent

66. SPPA 6010 Advanced Speech Science 65 Resonance refers to Natural vibrating frequency of a system The ability of a vibrating system to force another system into vibration

67. SPPA 6010 Advanced Speech Science 66 Resonance Acoustic (Cavity) Resonators Transmit sound frequencies with more or less efficiency, depending upon the physical characteristics Therefore, they act as filters, passing through (and even amplifying) some frequencies and attentuating others.

68. SPPA 6010 Advanced Speech Science 67 Resonance Acoustic (Cavity) Resonators And since they act as filters, they have most of the same features of a filter, even though we might use different names. Center frequency is often termed the resonant frequency. Frequency response curve often termed the resonance curve. Resonators may be sharply or broadly “tuned” which refers to the roll-off frequency

69. SPPA 6010 Advanced Speech Science 68 Resonator Features Sharply tuned Broadly tuned

70. SPPA 6010 Advanced Speech Science 69 Resonator Features An example of the resonance characteristics of the human vocal tract Frequency Gain

71. SPPA 6010 Advanced Speech Science 70 Learning Objectives Explain what the decibel is and why it is a preferred way to quantify amplitude

72. SPPA 4030 Speech Science71 Signal amplitude vs. Signal loudness The bigger the signal – the louder the signal Loudness is our perception of signal amplitude

73. SPPA 4030 Speech Science72 What units do we use to measure signal amplitude? Up to this point, we’ve used pressure pressure = force/area cgs units = 1 dyne/cm 2 = 1 barye = 0.1 pascal

74. SPPA 4030 Speech Science73 What units do we use to measure signal amplitude? Size may also be represented using intensity Intensity = Power/area –Power=Work/time –Work=Force*distance Units: watts/m 2 – not cgs

75. SPPA 4030 Speech Science74 Pressure-Intensity Relation Intensity is proportionate to Pressure 2

76. SPPA 4030 Speech Science75 What is the decibel scale? We use the decibel scale to represent signal amplitude We are used to using measurement scales that are absolute and linear The decibel scale is relative and logarithmic

77. SPPA 4030 Speech Science76 Linear vs. logarithmic Linear scale: 1,2,3… For example, the difference between 2 and 4 is the same as the difference between 8 and 10. We say these are additive

78. 77 Linear vs. logarithmic Logarithmic scales are multiplicative Recall from high school math and hearing science 10 = 10 1 = 10 x 1 100 = 10 2 = 10 x 10 1000= 10 3 = 10 x 10 x 10 0.1 = 10 -1 = 1/10 x 1 Logarithmic scales use the exponents for the number scale log 10 10 = 1 log 10 100 = 2 log 10 1000=3 log 10 0.1 = -1

79. SPPA 4030 Speech Science78 Logarithmic Scale base doesn’t have to be 10 In the natural sciences, the base is often 2.7… or e

80. SPPA 4030 Speech Science79 Logarithmic Scale Why use such a complicated scale? –logarithmic scale squeezes a very wide range of magnitudes into a relatively compact scale –this is roughly how our hearing works in that a logarithmic scales matches our perception of loudness change

81. SPPA 4030 Speech Science80 For example, linearlog 110 2100 31000

82. SPPA 4030 Speech Science81 Absolute vs. relative measurement Relative measures are a ratio of a measure to some reference Relative scales can be referenced to anything you want. decibel scale doesn’t measure amplitude (intensity or pressure) absolutely, but as a ratio of some reference value.

83. SPPA 4030 Speech Science82 Typical reference values Intensity –10 -12 watts/m 2 –Threshold for normal hearing at 1000 Hz Sound Pressure Level (SPL) –20 micropascals

84. SPPA 4030 Speech Science83 However… You can reference intensity/pressure to anything you want For example, Post therapy to pre therapy Sick people to healthy people Sound A to sound B

85. SPPA 4030 Speech Science84 Now, let us combine the idea of logarithmic and relative… bel= log 10 (I m / I r ) I m –measured intensity I r – reference intensity A bel is pretty big, so we tend to use decibel where deci is 1/10. So 10 decibels makes one bel dB IL = 10log 10 (I m / I r )

86. SPPA 4030 Speech Science85 Intensity vs. Pressure Intensity is difficult to measure. Pressure is easy to measure – a microphone is a pressure measuring device. Intensity is proportionate to Pressure 2

87. SPPA 4030 Speech Science86 Extending the formula to pressure Using some logrithmic tricks, this translates our equation for the decibel to dB SPL = (2)(10)log 10 (P m / P r ) = 20log 10 (P m / P r )