1. CHAPTER 3 SOUND TRANSMISSION

2. Sound in a Medium w Vibrating object displaces molecules in medium w molecules move back and forth w “bump” into others transmitting vibration thru medium

3. In the Medium: w We have both OSCILLATION of particles w and w TRANSMISSION of energy (or propagation)

4. Particle Motion w In Air, in line with transmission-- LONGITUDINAL w On Water, perpendicular to transmission-- TRANSVERSE

5. Displacement of Molecules in the Medium w creates areas of more molecules w --increased density--CONDENSATION w and areas of fewer molecules w --decreased density--RAREFACTION

6. Because We have Transmission: w We can talk about how fast sound travels in the medium = SPEED OF SOUND or c w Depends on medium, temperature, density, state w In Air = 344 meters/sec or 1100 feet/sec

7. Sound Travels Out From the Source In All Directions (at the same speed) So, Until Sound Encounters some object, the “wavefront” is spherical

8. We Can Also Talk About: w Distance Traveled during each cycle w = WAVELENGTH λ = c/f Wavelength = speed of sound / frequency

9. Wavelength Questions: What is the wavelength in meters of a 1720 Hz sound traveling in air? What is the wavelength in meters of an 86 Hz sound traveling in air?

10. Question 1: Freq = 1720 cyc/sec, c = 344 m/sec wavelength = c/f =344m/sec /1720 cyc/sec =0.2 m/cyc

11. Question 2: Freq = 86 cyc/sec, c = 344 m/sec wavelength = c/f = 344m/sec /86 cyc/sec = 4 m/cyc

12. When Talking about Amplitude: Remember Power is Rate at which Work is done (Work /Time = Power) But the power in sound doesn’t all travel the same direction Only some of it reaches you.

13. Therefore, we are more interested in: How much Sound Power there is in a given area (e.g., the opening of ear canal, microphone) New term: INTENSITY = Power/Area

14. Remember : Sound Power is spread over the Wavefront So the farther you are from the sound source: the larger the area over which power is spread the smaller the intensity

15. Intuitively, we all know this The closer you are, the louder the sound The farther away you are, the softer the sound

16. The Physics of the Situation: The relation between distance and intensity is an example of THE INVERSE SQUARE LAW Intensity = 1/distance 2

17. WHY? Surface area of sphere = 4 Pi r 2 In this case r = distance The area is proportional to distance squared

18. Change in Intensity = old d 2 / new d 2

19. EXAMPLE: w Moving from 100 m to 200 m away from source w Delta I = 100 2 /200 2 w = 1 x 10 4 /4 x 10 4 = 1/4 =0.25

20. Decibel Notation w Intensity is measured in Watts/cm 2 w Range of : w Just Audible 10 -16 W/cm 2 w to to w Just Painful 10 -4 W/cm 2

21. Can You Imagine? w 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…” w MR. SMITH: “ZZZZZZZZZZZZZ”

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

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

24. What is a log? w Log (x) = power you would raise 10 to to get x w e.g., log (10) = 1 w because 10 1 = 10 w or, log (0.01) = -2 w because 0.01 = 10 -2 w You can use a calculator to obtain logs

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

26. The Reference Value for Intensity Level w is 1 x 10 -16 Watts/cm 2 w Bels IL = log ( Im/ 1 x 10 -16 W/cm 2 ) w Where Im = measured intensity

27. The Range of Human Hearing w Detection w 10 -16 W/cm 2 OR 0 Bels w Pain w 10 -4 W/cm 2 OR 12 Bels

28. The Bel Is Too Gross a Measure For Us w So, We work in TENTHS OF BELS w The DECIBEL (dB) w dB IL = 10 log ( Im/ 1 x 10 -16 W/cm 2 )

29. EXAMPLE: w What is IL of sound with absolute intensity of 2 x 10 -16 W/cm 2 ? w = 10 log (2 x 10 -16 W/cm 2 / 1 x 10 -16 W/cm 2 ) w = 10 log (2) w = 10 (0.3010) w = 3 dBIL

30. Example--Relative Change w How will the intensity level change if you move to twice as far from a source? w We know that intensity change = old dist 2 /new dist 2 w = 1/4 or 0.25 w dB IL = 10 log (0.25) = 10 (-0.5991) = 6 dB

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

32. IMPEDANCE w The opposition to vibration, or w What, other than motion, happens to your applied force? w That is what do you have to overcome?

33. Impedance has 3 components: w Resistance: Energy lost to heat through friction (R) w Mass Reactance: Energy taken to overcome inertia (Xm) w Stiffness Reactance: Energy taken to overcome restoring force (Xs)

34. Impedance and Frequency: w Resistance is generally the same across frequency w Reactance Components change with frequency

35. Reactance and Frequency: w Mass reactance is greater at high frequencies w --it’s harder to get massive objects to vibrate quickly w Stiffness reactance is greater at low frequencies w --it’s harder to get stiff objects to vibrate slowly

36. Mass and Stiffness Reactance Resonant Freq.

37. At Resonant Frequency w Mass and Stiffness Reactance Cancel w Only opposition to vibration is Resistance w In Forced Vibration, you get the most vibratory amplitude for amount of force applied

38. Sound Wave Phenomena Reflection-bouncing off an object Absorption-sound trapped (absorbed) by an object Diffraction-spreading of sound into area beyond an object Refraction-bending of sound waves in a medium

39. Sound Encountering an Object: Transmission-setting object into vibration Reflection-sound bounces back Absorption-sound becomes trapped in gaps of surface of object

40. Reflected and Incident Sound Meet Producing INTERFERENCE Where the two waves meet in phase, the intensity doubles --Constructive Interference Where they meet out of phase, cancellation --Destructive Interference

41. Getting around an Object: w depends on size of object and wavelength of sound  λ > object’s diameter, sound passes by  λ < object’s diameter, sound blocked w Area of reduced or no sound energy is “sound shadow”

42. Diffraction Sound passing an object will spread to fill in area beyond it, behaving as if the edge of the object were the sound source.

43. Refraction the bending of the sound’s path produced by changes in medium e.g., temperature changes will bend path of sound propagation

44. Sound Fields FREE FIELD = no objects in medium ANECHOIC CHAMBER = room with highly absorptive walls; an attempt to create a free field.

45. Sound Fields (cont’d) SOUND TREATED ROOM = has somewhat absorptive walls, produces some reflections REVERBERATION ROOM = highly reflective walls set at odd angles; many reflections and complex interactions. Creates a uniform (diffuse) sound field.

46. Reverberation: Persistence of sound in a sound field after the source is turned off = time taken for intensity to drop to 1 millionth of initial value Reverberation ≈ ROOM VOL./ABSORPTION COEF.

47. Reverberation Time Least for Anechoic Chamber Most for Reverberation Room Longer for larger rooms with reflective walls

48. Earphones Miniature loudspeakers to introduce sound into the ear. Supra-aural (sits on the pinna) Insert (sits within external canal) Calibrated in “artificial ears” (6cc or 2cc couplers)

49. The Doppler Effect w Change in the effective frequency produced by motion of the sound source. w (or by motion of the listener) w Toward >>higher frequency w Away >> lower frequency

50. The Doppler Effect 1

51. The Doppler Effect 2

53. Resonance Helmholtz Resonators simulate influence of mass and compliance (stiffness) on resonance. Tube and Cavity. Mass component--inversely proportional to resonant freq Compliance component--directly prop. to resonant freq Resistance -- doesn’t affect resonant freq, but produces broader tuning

54. Standing Waves Interaction between incident and reflected waves Produces areas of : constructive interf. --ANTINODE destructive interf. --NODE

55. Incident & Reflected Sound Meet w Incident in Black w Reflected in Pink w Type of Interference varies with position.

56. Standing Wave Illustration

57. Standing Waves (cont’d) Intensity varies with position Position of nodes, antinodes depends on frequency Distance from node to antinode is 1/4 λ Distance from one node to the next is ½ λ

58. Pipes produce standing waves w closed pipes —antinode at open end and node at closed end w open pipes — antinode at each open end w closed pipe, length = ¼ λ w open pipe, length = ½ λ

59. Standing Waves in Pipes

60. A closed pipe only produces odd harmonics. w Frequency of harmonics = (n c)/4 L, w Where n=1, 3, 5,... w c = speed of sound w L is the length of the pipe. w In music, harmonics are called overtones.