A tutorial on the four general classes of Active Acoustic Spectroscopy

1. A tutorial on the four general classes of Active Acoustic Spectroscopy T G Leighton Institute of Sound and Vibration Research University of Southampton

2. If one wishes to measure a bubble population, one of the most useful methods is active acoustic bubble spectroscopy. In this, a sound field is projected into the bubbly liquid. The interaction of the sound field with the bubbles produces an acoustic signal which may be inverted to estimate the numbers of bubbles present and their radii. Introduction: (This can be contrasted to passive acoustic bubble spectroscopy[Sarina, link this to raindrop ppt] where the bubble population is diagnosed simply by listening to the emissions made by the bubbles: no incident sound field is projected at the bubbles).

3. In summary therefore, to achieve active acoustic bubble spectroscopy one must undertake 3 procedures: [1] Insonify bubble population [2] Monitor effect on sound speed, attenuation, scatter [3] Invert acoustic data using suitable model Because of this, the various methods of active acoustic bubble spectroscopy have features in common, which will be colour coded in the following schematic:

4. All have a signal generator and sound source (Yellow) Signal generator Active acoustic bubble spectroscopy Sound source

5. In the following schematics the signal which is generated to drive the bubbles into pulsation will be called the ‘pump frequency’ (wp). In actual fact, it is often not a single frequency but a series of tones, a chirp, for a pseudo-random (pn) signal. In general, the larger at the frequency band covered by the pump frequencies, the greater the range of bubble sizes that can be measured. Active acoustic bubble spectroscopy

6. All of the four general types of systems which will be illustrated here also have, in addition to a signal generator and sound source (Yellow), a sensor such as hydrophone (Green) which is used to measure the acoustic signal. Active acoustic bubble spectroscopy

7. The acoustic waveform (shown in White) is emitted from the sound source (Yellow). If bubbles are not present, it generates a particular signal at the detector (Green). Active acoustic bubble spectroscopy

8. However bubbles (shown in the Blue) may indeed be present. Their interaction with the incident acoustic wave (White) will change it…. Active acoustic bubble spectroscopy

9. …and we use the Red colour to indicate the acoustic field after it has been modulated by the bubble population. Active acoustic bubble spectroscopy

10. The change in the received Acoustical signal which the presence of bubbles induces is used to infer the number of bubbles present, and their sizes,in the man and written in green. This first system, for example, uses the changes in signal amplitude and travel time when an acoustic pulse is propagated from a source to receiver (or an array of receivers). Active acoustic bubble spectroscopy

11. The second system to be discussed generates a sound field in some resonant cavity, set up for example between two parallel plates. Active acoustic bubble spectroscopy

12. The acoustic monitor might be a hydrophone (Green) position that some location within the resonant cavity. Active acoustic bubble spectroscopy

13. Instead of projecting an acoustic pulse, as in the first category of system to be discussed, the “incident sound field in the absence of bubbles” (White) corresponds to be resonant modes of the cavity. Active acoustic bubble spectroscopy

14. When bubbles are present, they impart to the water a different sound speed and absorption than it would have and the bubble-free conditions. Active acoustic bubble spectroscopy

15. Since the resonant cavity is of fixed size, then a change in the sound speed causes a shift in the resonant frequency of the modes. Similarly, a bubble-induced increase in the losses of the resonance cavity increases the bandwidth (and reduces the quality factor) of each resonant mode. Active acoustic bubble spectroscopy

16. The bubble size distribution can be inferred from these changes to the frequencies and quality factors of resonator modes. Active acoustic bubble spectroscopy

17. The third general type of system is rather different. It does not use a pump frequency. Instead two acoustic beams, both having frequencies very much higher than the resonances of any bubbles present, are projected into the water. The first has frequency w1 … Active acoustic bubble spectroscopy

18. … and the second has frequency w2 Active acoustic bubble spectroscopy

19. Under linear conditions the only frequencies that might be detected in the water would be w1 and w2 Active acoustic bubble spectroscopy

20. However the presence of bubbles enhances the nonlinearity of the propagation… Active acoustic bubble spectroscopy

21. …causing sum- and difference-signals to be generated at w1+/- w2 Active acoustic bubble spectroscopy

22. First-order interpretation is that any signal detected at w1-w2 has been generated by those bubbles whose resonance frequency corresponds to this difference frequency. The amplitude of the dejected difference frequency is therefore related to the number of bubbles resonant at it. Active acoustic bubble spectroscopy

23. The fourth category of detection system also stands out a signal at wi, the ’imaging’ frequency (which is very much higher than the resonances of any bubbles present). Active acoustic bubble spectroscopy

24. As with the third category of detection system, a second acoustic signal is also emitted. However unlike the case in the third category, here this second signal is at the pump frequency. Active acoustic bubble spectroscopy

25. As with the third category, if the system where an entirely linear then the only frequencies in the dejected signal would correspond to the two frequencies that were emitted. Active acoustic bubble spectroscopy

26. However as before, bubbles increase the nonlinearity of the propagation… Active acoustic bubble spectroscopy

27. …causing sum- and difference-signals to be generated at wi+/- wp . Active acoustic bubble spectroscopy

28. …causing sum- and difference-signals to be generated at wi+/- wp . The amplitudes of these signals are then related to the number of bubbles which are resonant at wp . Active acoustic bubble spectroscopy