1. 1 ME 660 Intermediate Acoustics Instructor:Dr. Joseph Vignola Office:Pangborn G43 Phone:202-319-6132, e-mail: vignola@cua.edu Time (section 1):Tuesdays, 6:35-9:00PM Time (section 2):Thursdays, 1:35-4:00PM Office Hours: Tuesdays 1:00 -2:00, (or anytime I’m in my office or the lab which is most of normal business hours) Web pages: http://josephfv.googlepages.com/ http://josephfv.googlepages.com/ http://faculty.cua.edu/vignola/

2. 2 Line Source Directivity Now lets think about a source that is long relative to the wavelength as shown. This type of source is important in ultrasound and oceanographic application and it helps us build up to more complex source geometries. A cylindrical line source, length L, that vibrates radially is shown on the x-axes of a coordinate system.

3. 3 Line Source Directivity Now lets think about a source that is long relative to the wavelength as shown. Assume that the surface vibrates radially with a surface velocity each little bit of the line source has an incremental volume velocity (source strength)

4. 4 Line Source Directivity Now lets think about a source that is long relative to the wavelength as shown. Assume that the surface vibrates radially with a surface velocity each little bit of the line source has an incremental volume velocity (source strength)

5. 5 Line Source Directivity Now lets think about a source that is long relative to the wavelength as shown. Evaluation this integral is a little messy but if we assume that is and independent of x then the expressing becomes easier to work with. This is the case if is moderately large relative to a wavelength

6. 6 Line Source Directivity Now lets think about a source that is long relative to the wavelength as shown. The integral at the end of this expression can be found in tables of integrals This part (without the first L) is referred to as the directivity

7. 7 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

8. 8 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

9. 9 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

10. 10 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

11. 11 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

12. 12 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

13. 13 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

14. 14 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

15. 15 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

16. 16 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

17. 17 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

18. 18 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

19. 19 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

20. 20 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

21. 21 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

22. 22 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

23. 23 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

24. 24 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

25. 25 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

26. 26 Line Source Directivity When the kL is small, (length is smaller then the wavelength). the line source radiates uniformly in all directions.

27. 27 Line Source Directivity Only now that kL>=1 Do we see any directivity

28. 28 Line Source Directivity For kL>=1 we see that the radiated pressure is not reduced in the direction perpendicular to the line source

29. 29 Line Source Directivity …but is starting to be reduced along the axial direction of the line source

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35. 35 Line Source Directivity Along the direction perpendicular (θ = 0°) to the line source, a receiver sees all the points as essentially the same distance away. The pressure from all point on the source add coherently (constructively )

36. 36 Line Source Directivity Sound rays traveling along the direction (θ = 90°) of the line source, travel different distances to get to a receiver. This means they don’t add coherently and we see some cancelations.

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43. 43 Line Source Directivity When ka = 2π we have complete cancelation in axial direction (θ = 90°) When θ goes from 0° to 90° the agreement of the outer (red) sine function goes from 0 to π

44. 44 Line Source Directivity When ka > 2π we see the appearance of a additional lobe(s) because the argument of the outer (red) sine function can now be greater then π.

45. 45 Line Source Directivity …and the main lobe gets narrower and narrower.

46. 46 Line Source Directivity When 2π > ka > 4π we will expect 2 lobes.

47. 47 Line Source Directivity When 2π > ka > 4π we will expect 2 lobes. The second lobe only reaches it full amplitude when ka > 3π

48. 48 Line Source Directivity

49. 49 Line Source Directivity When ka = 4π we have two complete lobes and cancelation in axial direction (θ = 90°) When θ goes from 0° to 90° the agreement of the outer (red) sine function goes from 0 to 2π

50. 50 Line Source Directivity As we continue to increase ka past 4π we we see more lobes …and the primary lobe get narrower

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