1. SPPA 4030 Speech Science1 Sound Physics

2. SPPA 4030 Speech Science2 Outline  What is sound?  Graphic representation of sound  Classifying sounds  The Acoustic Filter  Resonance  The decibel

3. SPPA 4030 Speech Science3 What is sound?  It may be defined as the propagation of a pressure wave in space and time.  propagates through a medium

4. SPPA 4030 Speech Science4 Sound-conducting media  Medium is composed of molecules  Molecules have “wiggle room”  Molecules exhibit random motion  Molecules can exert pressure AB

5. SPPA 4030 Speech Science5 Spring Mass Model  Mass (inertia)  Elasticity  Friction

6. SPPA 4030 Speech Science6 Model of air molecule vibration (Time 1) Rest positions Air molecules sitting side by side

7. SPPA 4030 Speech Science7 Model of air molecule vibration (Time 2)

8. SPPA 4030 Speech Science8 Model of air molecule vibration (Time 3)

9. SPPA 4030 Speech Science9 Model of air molecule vibration (Time 4)

10. SPPA 4030 Speech Science10 Model of air molecule vibration (Time 5)

11. SPPA 4030 Speech Science11 Model of air molecule vibration Time 1 2 3 4 5 Distance abcd

12. 12 Wave action of molecular motion Time 1 2 3 4 5 Distance

13. SPPA 4030 Speech Science13 Amplitude waveform Position Time

14. SPPA 4030 Speech Science14 Amplitude waveform Amplitude Time Question: How long will this last?

15. SPPA 4030 Speech Science15 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?

16. SPPA 4030 Speech Science16 For example… Pressure Time

17. SPPA 4030 Speech Science17 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)

18. SPPA 4030 Speech Science18 Phase

19. SPPA 4030 Speech Science19 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

20. SPPA 4030 Speech Science20 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

21. SPPA 4030 Speech Science21 Frequency representation: The octave  Octave shift: doubling or halving of frequency  Non-linear

22. SPPA 4030 Speech Science22 Spatial variation in pressure wave wavelength ( ) is the distance covering adjacent high and low pressure regions

23. SPPA 4030 Speech Science23 For example… Distance Wavelength ( ) Pressure

24. SPPA 4030 Speech Science24 Relation between frequency and wavelength =c/F where : wavelength F: is the frequency c: is sound speed in medium (33,600 cm/sec)

25. SPPA 4030 Speech Science25 Additional Concepts  Propagation of waves Transmission Absorption Reflection Reverberation

26. SPPA 4030 Speech Science26 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

27. SPPA 4030 Speech Science27 Same sound, different graphs Time domain Frequency domain From Hillenbrand

28. SPPA 4030 Speech Science28 Classification of sounds  Number of frequency components Simple Complex  Relationship of frequency components Periodic Aperiodic  Duration Continuous Transient

29. SPPA 4030 Speech Science29 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

30. SPPA 4030 Speech Science30 Simple periodic sound: Graphic appearance From Hillenbrand

31. SPPA 4030 Speech Science31 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

32. SPPA 4030 Speech Science32 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’

33. SPPA 4030 Speech Science33 Complex periodic sounds: Graphic appearance From Hillenbrand

34. SPPA 4030 Speech Science34 (Complex) Aperiodic sounds  Complex: > one frequency component  Aperiodic: Does not repeat itself  Frequency components are not systematically related  May be Continuous Transient

35. SPPA 4030 Speech Science35 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’

36. SPPA 4030 Speech Science36 Aperiodic sounds: Graphic appearance From Hillenbrand

37. SPPA 4030 Speech Science37 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

38. SPPA 4030 Speech Science38 The “envelope” of a sound wave  Amplitude 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

39. SPPA 4030 Speech Science39 Amplitude envelope From Hillenbrand

40. SPPA 4030 Speech Science40 Spectrum envelope From Hillenbrand

41. SPPA 4030 Speech Science41 Amplitude Spectrum: Window Size  “instantaneous” vs. average spectrum

42. SPPA 4030 Speech Science42 “Instantaneous” Amplitude Spectra

43. SPPA 4030 Speech Science43 (Long Term) Average Amplitude Spectrum

44. SPPA 4030 Speech Science44

45. SPPA 4030 Speech Science45 What is a filter?

46. SPPA 4030 Speech Science46 “Acoustic” Filter  holds back (attenuates) certain sounds and lets other sounds through - selective.

47. SPPA 4030 Speech Science47 Why might we be interested in filters?  human vocal tract acts like a frequency selective acoustic filter  helps us understand how speech is produced and perceived.

48. 48 Frequency Response Curve (FRC) Frequency lowhigh Gain + - Center frequency lower cutoff frequency upper cutoff frequency passband 3 dB

49. SPPA 4030 Speech Science49 Operation of a filter on a signal NOTE: Amplitude spectrum describes a sound Frequency response curve describes a filter

50. SPPA 4030 Speech Science50 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

51. SPPA 4030 Speech Science51 Low Pass Filters Frequency lowhigh Gain + -

52. SPPA 4030 Speech Science52 High Pass Filters Frequency lowhigh Gain + -

53. SPPA 4030 Speech Science53 Band Pass Filter Frequency lowhigh Gain + -

54. SPPA 4030 Speech Science54 Resonance

55. SPPA 4030 Speech Science55 Free vibration  objects tend to vibrate at a characteristic or resonant frequency (RF)

56. SPPA 4030 Speech Science56 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

57. SPPA 4030 Speech Science57 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

58. SPPA 4030 Speech Science58 Resonance refers to  Natural vibrating frequency of a system  The ability of a vibrating system to force another system into vibration

59. SPPA 4030 Speech Science59 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.

60. SPPA 4030 Speech Science60 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

61. SPPA 4030 Speech Science61 Resonator Features Sharply tuned Broadly tuned

62. SPPA 4030 Speech Science62 Resonator Features An example of the resonance characteristics of the human vocal tract Frequency Gain

63. SPPA 4030 Speech Science63 Sound pressure, intensity and the decibel scale

64. SPPA 4030 Speech Science64 Signal amplitude vs. Signal loudness  The bigger the signal – the louder the signal  Loudness is our perception of signal amplitude

65. SPPA 4030 Speech Science65 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

66. SPPA 4030 Speech Science66 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

67. SPPA 4030 Speech Science67 Pressure-Intensity Relation  Intensity is proportionate to Pressure 2

68. SPPA 4030 Speech Science68 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

69. SPPA 4030 Speech Science69 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

70. 70 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

71. SPPA 4030 Speech Science71 Logarithmic Scale  base doesn’t have to be 10  In the natural sciences, the base is often 2.7… or e

72. SPPA 4030 Speech Science72 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

73. SPPA 4030 Speech Science73 For example, linearlog 110 2100 31000

74. SPPA 4030 Speech Science74 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.

75. SPPA 4030 Speech Science75 Typical reference values  Intensity 10 -12 watts/m 2 Threshold for normal hearing at 1000 Hz  Sound Pressure Level (SPL) 20 micropascals

76. SPPA 4030 Speech Science76 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

77. SPPA 4030 Speech Science77 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 )

78. SPPA 4030 Speech Science78 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

79. SPPA 4030 Speech Science79 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 )