More on Intensity

1. More on Intensity • Remember the Units for I • Watts / Meter2 • What is “Watts” a measure of? • What is “Meter2” a measure of?

2. A sound source is doing work on the air. It’s generating power. That power spreads outward in a sphere, spread out on it’s surface.

3. Sound waves carry energy. Energy per second is the power of the wave. The sound intensity is defined as the power that passes through a surface divided by the area of that surface.

4. area of sphere

5. Problem • A person stand 3 meters away from a speaker generating 45 watts of power. • What is the intensity heard by the person?

6. Problem • A person stand 3 meters away from a speaker generating 45 watts of power. • What is the intensity heard by the person? • What is the dB level?

7. Problem • A person stand 3 meters away from a speaker generating 45 watts of power. • What is the farthest a person can stand from this speaker and still hear it?

8. Diffraction • Question – • Light and sound are both waves. • If I shine a flashlight out the door, the light goes in a straight line. • If I shout out the door, the sound waves will curve both direction down the hall. • Why is this?

9. Diffraction If a wave (any wave) passes through a gap, it will spread out as if the gap were a point source of the wave.

10. Diffraction Works best when the gap matches the wavelength of the wave. Tapers off if the gap gets significantly wider than the wavelength.

11. Diffraction • Back to the question – • Light – l ~ nanometers • Sound - l ~ meters • Which will diffract most effectively through a doorway?

12. Phase What is the difference between these two waves?

13. Phase Same amplitude. Same wavelength. The only difference is the phase.

14. Phase Phase is the fraction of the wave cycle that has elapsed.

15. Phase What are some units for “fraction of a cycle?”

16. Phase What are some units for “fraction of a cycle?” Radians, Degrees, and Revolutions.

17. Phase difference Often times, we will want to compare the difference in phase of two waves to see how they will combine.

18. Phase difference. Two waves completely in phase. Crests Line up. Phase difference = 0 Two waves completely out of phase. Crest lines up with trough. Phase difference = 180˚, or ∏ rads, or 1/2 revolution.

19. Phase difference If two with different phases interfere, the amplitude of the combined wave will be between the sum of the original two and the difference of the original two.

20. Interference of sound waves • The phase of a wave as it reaches a point depends on the distance from that point to the source.

21. Interference of sound waves • The phase of a wave as it reaches a point depends on the distance from that point to the source. • The phase difference between sound from two sources depends on the path difference between those two sources.

22. Interference of Sound Waves Constructive interference occurs when compressions from both sources hit simultaneously. Or the two sources are in phase at that point. Path difference between two waves’ motion is some integer multiple of wavelengths Path difference = nλ (n= 0, 1, 2, 3 etc…) Destructive interference occurs when compression lines up rarefaction. Or the two sources are out of phase at that point. Path difference between two waves’ motion is an odd half wavelength Path difference = (n + ½)λ

23. What does this look like? • Two souces • Red is compression • Blue is rarefaction • Light blue lines never get a compression or rarefaction. • They are “dead zones” and never hear either source.

24. Beats • Two waves, with slightly different frequencies, interfere. What will this sound like?

25. Beats

26. Beats Beats are alternations in loudness, due to interference Alternates between constructive and destructive interference. The beat frequency equals the difference in frequency between the two sources:

27. Two in-phase loudspeakers, A and B, are separated by 3.20 m. A listener is stationed at C, which is 2.40 m in front of speaker B. Both speakers are playing identical 214-Hz tones, and the speed of sound is 343 m/s. Does the listener hear a loud sound, or no sound?

28. Calculate the path length difference. Calculate the wavelength. Because the path length difference is equal to an integer (1) number of wavelengths, there is constructive interference, which means there is a loud sound.

29. Two in-phase loudspeakers, A and B, are separated by 3.20 m. A listener is stationed at C, which is 2.40 m in front of speaker B. The tone changes to a frequency of 321 hz. What does he hear?

30. Calculate the path length difference. Calculate the wavelength. ΔL = 1.6. 1.06/1.07 = 1.5 An “odd half” wavelength means destructive interference, so less sound.

31. Remember Standing Waves

32. Remember Standing Waves • On a string or spring, a wave interfered with it’s own reflection. • A standing wave occurred if each end of the string or spring was a node.

33. Standing Waves in Air Columns If end of the air column is closed, a node must exist since the movement of the air is restricted. If the end is open, an antinode must exist

34. Tube Open at Both Ends

35. Tube Open at Both Ends

36. Resonance in Air Column Open at Both Ends In a pipe open at both ends, the natural frequency of vibration forms a series whose harmonics are equal to integer multiples of the fundamental frequency

37. Problem • A Flute is 61 cm long. If the speed of sound is 340 m/s, find the frequency of the first harmonic.

38. Tube Closed at One End

40. Resonance in an Air Column Closed at One End The closed end must be a node The open end is an antinode Only odd harmonics exist.

41. Problem • A pipe organ uses pipes of different lengths to create different tones. Each pipe produces one tone, and uses an Open-Closed standing wave air column. Find the first three frequencies of the “4-foot” (1.22 m ) pipe, if the speed of sound is 340 m/s.

42. http://www.youtube.com/watch?v=HpovwbPGEoo

43. 449 Hz • What harmonic is this? • Are the ends open or closed? • How can you tell?

44. As f increases • What happens to l?