Sound Transmission: Vibrations, Mediums, and Wavelengths

1. CHAPTER 3 SOUND TRANSMISSION

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

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

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

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

6. Because We have Transmission: • We can talk about how fast sound travels in the medium = SPEED OF SOUND or c • Depends on medium, temperature, density, state • 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: • Distance Traveled during each cycle • = WAVELENGTH • = 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/secwavelength = 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/distance2

17. WHY? • Surface area of sphere = 4 Pi r2 • In this case r = distance • The area is proportional to distance squared

18. Change in Intensity • = old d2 / new d2

19. EXAMPLE: • Moving from 100 m to 200 m away from source • Delta I = 100 2/200 2 • = 1 x 104/4 x 104 • = 1/4 • =0.25

20. Decibel Notation • Intensity is measured in Watts/cm2 • Range of : • Just Audible 10-16 W/cm2 • to to • Just Painful 10-4 W/cm2

21. 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”

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

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

24. 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

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

26. 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

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

28. 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)

29. 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

30. 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

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

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

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

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

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

36. Mass and Stiffness Reactance Resonant Freq.

37. At Resonant Frequency • Mass and Stiffness Reactance Cancel • Only opposition to vibration is Resistance • 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: • depends on size of object and wavelength of sound • λ> object’s diameter, sound passes by • λ< object’s diameter, sound blocked • 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 • Change in the effective frequency produced by motion of the sound source. • (or by motion of the listener) • Toward >>higher frequency • Away >> lower frequency

50. The Doppler Effect 1