ACOUSTICS

1. ACOUSTICS • Sound in a Medium • Sound Wave Phenomena • Sound Fields • Earphones • Resonance and Standing Waves

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. EXAMPLE OF SOUND WAVES http://rustam.uwp.edu/GWWM/sound_waves.html

13. 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.

14. 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

15. 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

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

17. The Physics of the Situation: • The relation between distance and intensity is an example of • THE INVERSE SQUARE LAW • Intensity = 1/distance2

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

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

20. 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

21. 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

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

23. 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

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

25. Diffraction • Sound passing an object will spread to fill in area beyond it.

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

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

28. 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.

29. 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.

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

31. 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)

32. 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

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

34. Standing Wave Illustration

35. Standing Waves (cont’d) • Intensity varies with position • Position of nodes, antinodes depends on frequency

36. Pipes produce standing waves • closed pipes —antinode at open end and node at closed end • open pipes — antinode at each open end • closed pipe, length = ¼ l • open pipe, length = ½ l

37. Standing Waves in Pipes

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