2. 1414 Ball Sound Jakub Chudík 4

3. 1414 Task When two hard steel balls, or similar, are brought gently into contact with each other, an unusual ‘chirping’ sound may be produced. Investigate and explain the nature of the sound. 2

4. 1414 Different Balls 3 Chosen for the longest duration and the lowest prevalent frequency Collisions between different balls and one large steel ball

5. 1414 In our presentation 4 Recreate the sound Nature of the sound Examine the sound

6. 1414 Possible sources 5 Impulsive translational acceleration Vibration of the balls

7. 1414 Vibrations for steel balls of 5cm diam. 6 Mode number Natural frequency (kHz) 151.8 268.3 377 493.1 597 698.5 7118.7 8128.2 9136.7 10138.3 Lowest frequency is 51,8 kHz K. Mehraby et al. „Impact noise radiated by collision of two spheres“, Journal of Mechanical Science and Technology 25 (7) (2011) Limit of human ear is 18-20 kHz Lowest frequency for our balls is 64,75 kHz Vibrations of the balls certainly do not contribute to audible sound!

8. 1414 Impulsive translational acceleration One oscillating sphere Two colliding spheres 7 K. Mehraby et al. „Impact noise radiated by collision of two spheres“, Journal of Mechanical Science and Technology 25 (7) (2011)

9. 1414 Impulsive translational acceleration One collisionTwo colliding spheres 8 K. Mehraby et al. „Impact noise radiated by collision of two spheres“, Journal of Mechanical Science and Technology 25 (7) (2011)

10. 1414 9 Recreate the sound Nature of the sound Examine the sound

11. 1414 Our apparatus 10

12. 1414 Sound analysis 11 Whole sound made of individual collisions

13. 1414 Sound of individual collisions 12

14. 1414 Sound of individual collisions Decreasing amplitude Individual collisions are similar But the chirping has a rising tone 13 Time between collisions is decreasing

15. 1414 Spectral analysis of our measured chirping 14 Time Frequency

16. 1414 Spectrum of chirping sound (FFT) 15 First few collisions: distinguishable “Fluent” sound

17. 1414 Spectrum of chirping sound (FFT) 16 Peaks rising in time

18. 1414 Time between collisions 17

19. 1414 Frequency of collisions in time 18

20. 1414 Spectrum of chirping sound (FFT) 19 Pattern is caused by increase of frequency of collisions Peaks rise in time … if you remember…

21. 1414 =n* Frequency of collisions

22. 1414 =n* Multiple of frequency of collisions

23. 1414 =n*

24. 1414

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26. 1414 25 Recreate the sound Nature of the sound Examine the sound

27. 1414 Ingredients for an artificial sound 1.Time of individual collisions 2.Impact speed for each collision –Determines loudness 3.Sound of a single collision 26

28. 1414 Simplified model of collisions Constant attractive force Time between 2 collisions: mass speed after the last collision Coefficient of restitution: Impact speed change: 27

29. 1414 Simplified model of collisions Impact speed decrease in time: –Suitable for fast chirping Speed before collisions: Time between collisions: 28

30. 1414 Reality check 29 Distortions caused by hitting the foam

31. 1414 Reality check 30

32. 1414 Reality check 31 Similar to real behavior!

33. 1414 Notable conclusions 32 LOUD quiet Loudness of the sound But not negligible But not negligible

34. 1414 Sound creation in Mathematica 33

35. 1414 Artificial vs. Real 34

36. 1414 Conclusion – Nature of sound Two options –Vibration of balls –Impulsive translational acceleration 35 Mode number Natural frequency (kHz) 151.8 268.3 377 493.1 597 698.5 7118.7 8128.2 9136.7 10138.3 Lowest frequency of our balls 113,5 kHz

37. 1414 Simplified model of collision Advanced theory –L. L. Koss, R. J. Alfredson: Generated authentic sound Conclusion – Analysis and Recreation 36

38. 1414 =n* Thank you for your attention

39. 1414 Sound of single collision K. Mehraby et al: “Impact noise radiated by collision of two spheres“ Journal of Mechanical Science and Technology, 2011 L. L. Koss, R. J. Alfredson: “Transient sound radiated by spheres undergoing an elastic collision” Journal of Sound and Vibration, 1972 38 –Fully theoretical & analytical solution –Underestimates the loudness for theta=90° –Otherwise good correlation –Finite elements method simulation –“Perfect” agreement with experiment

40. 1414 Fourier transform of ball’s motion Velocity potential for colliding balls Koss & Alfredson: Theory basis  Interaction of balls: ‒ Acceleration approximation:  Velocity potential for an oscillating sphere*: 39 *I. Malecki: Physical Foundations of Technical Acoustics (duration of contact)

41. 1414 Koss & Alfredson: results 40

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45. 1414 Different Balls 44 No principial difference in sound Sound differs in frequency and duration 6200 Hz 7000 Hz 8000 Hz 7700 Hz 5000 Hz

46. 1414 Sound analysis 45

47. 1414 Procedure of Fourier transform 46 Scanned area FFT size

48. 1414 47

49. 1414 Period of collisions 48 Similar to real behavior!!

50. 1414 49

51. 1414 Generating fake chirping sound Take 1 collision 50 And decreasing amplitude Paste 185 times with increasing frequency

52. 1414 Reality check 51 Generated Measured

53. 1414 Single collision – our measurement vs theory 52

54. 1414 Spectral analysis 53 Distinguish individual collisions Pattern caused by increasing frequency of the collisions

55. 1414 Our apparatus 54 Steel Balls: Radius: 1.43 cm Mass: 0.095 kg Colliding on soft foam Little energy losses due to damping

56. 1414 Single collision noise approximation 55 Real waveform

57. 1414 Chirping sound Subsequent Identical sounds 56 REAL chirping sound

58. 1414 Second verification method We can generate chirping sound by pasting the same single-collision- waveform one after another 57

59. 1414 Now we know the motion of the balls 58

60. 1414 Motion Origin Why do we hear the chirping? 59

61. 1414 Spectrum of one collision 60 Fourier transform Our model Let’s put the collisions together!

62. 1414 Spectrum of one moment of chirping 61 200Hz – frequency of collisions

63. 1414 62 Peak in time rising Time is increasing => frequency of collisions increasing