2010-06-05
Strange Speed of Sound Result
A quick experiment to assess the practicality of using commercial piezo sounder elements as ultrasonic transducers lead me to an odd result that I am yet to adequately explain. Knowing nothing much about ultrasonics other than piezo and magnetostrictive transducers are the most common I set off in my own blind attempt to launch some ultrasound into something and detect it again. Instead of investing in an expensive commercial transducer I decided to see how far I could get with whatever I had in the junkbox.
A pair of Kyocera piezos from Rockby were dismantled for a quick transmission experiment. Fine magnet wire was soldered to the transducers and the pair was taped to opposite sides of my solder sponge dampening wash bottle (below the water line) with a drop of water between the transducer face and the bottle wall as a coupling. One transducer was connected to a signal generator, and the other to the CRO, then the lash-up swept looking for supersonic resonances. The most prominent resonance was in the audible frequency range, at around 5.8 kHz, but a suitable ultrasonic resonance was located at 127.3 kHz. I was hoping for resonances in the MHz region to give me good spatial resolution in future experiments, but only very weak resonances were available above a few hundred kHz, and it is not yet clear if the HF resonances are ultrasonic or electromagnetic in nature (such is the state of my unshielded lash-up).
All looked well with the set-up until I noted the propagation delay of transient pings or CW tone bursts was much larger than expected. Doing the maths, it was found the velocity of propagation transducer-to-transducer was about 160 m/s! I was seeing twice the time of flight in air, and a velocity of about a tenth of the expected figure.
Assuming what I was seeing was propagation through the soft plastic rather than the liquid inside I tried launching pulses through my desk and along its length. Getting rather confusing velocity results (but delays linearly scaling with transducer separation) I tried yet another subject. A 1 metre long strip of 2x30 mm aluminium extrusion, coupling the transducers directly to each end, held in place with a little Bostik Blu-Tack.
Once again the measured velocity of propagation was lower than expected. The sound waves taking about 600 us to travel from one end of the bar to the other. This corresponds to 1700 m/s rather than the 5000 m/s expected for compression waves in Aluminium. Right order of magnitude at least, but still stubbornly ignorant of my expectations. Going back to first principles I computed the compression and shear wave velocities in Aluminium from its density, Young's and shear modulus. The figures agree well with the published figures of 5000 m/s and 3100 m/s. Even considering alloy differences I can't accept such enormous differences between the measured figure and the expected values, my experimental set-up must be flawed.
Even so, the delay scales beautifully with the path length. I can leave one transducer attached to the bar end and slide the other along its edge while watching the pulse delay on the CRO get longer or shorter in response. If I don't damp the bar by gripping it tightly I can see exponential decay of reverberating signals and what appears to be multipath cancellation effects that change quite dynamically even with no appreciable movement of the apparatus (suggesting quite short wavelength with respect to the wave-guide). Using my measured figure for velocity the corresponding wavelength would be about 13 mm, and 39 mm for the assumed figure of 5000 m/s. This means the bar is between 26 and 77 wavelengths long, implying it is reasonable that dispersion and multipathing might be observed.
I assume I am not accounting for something about my set-up or I am launching some other mode of sound propagation, perhaps a surface wave? Although I believed surface waves travel only a little slower than the shear wave velocity? The transducers are no doubt problematic, they are after all just ordinary piezo electric sounders that I have removed from their casings. They have a natural audio-frequency resonance far below the frequency I am experimenting with (I assume the AF resonance is the fundamental flexural mode with the outer edge as a node?). The transducer plate appears to be made of brass, which I calculate to have compression and shear wave velocities of about 3700 m/s and 2200 m/s respectively. The disk is about 30 mm in diameter, which is about 1 wavelength at 123 kHz. A numeric coincidence, or the cause of the strong 127 kHz resonance? I can not picture what mode it might be oscillating in at this frequency which the planar PZT element could excite? Maybe try dusting the plate with a fine powder while driving it hard?
In any case the transducers are likely completely unsuitable for ultrasonics experiments, especially coupling to solids. I have found little information online as to precisely what makes a good ultrasonic transducer, but I am proceeding with the assumption smaller is more likely to have a higher frequency response all things being equal? I would imagine the PZT element thickness is important too, probably a half-wave at the fundamental? Who knows what the field of my current devices looks like? I may try mounting one properly, fixed at its edge and backed with a dissipative material to hide the fixture impedance mismatch and kill the mechanical Q. The transducers ring a lot when driven by a transient, and the AF oscillations frustrate attempts to measure short propagation distances. Ideally I want a HF fundamental with a rapid decay.
One thing I want to try is direct induction of ultrasonic motion in metals with an RF field and a bias magnet. This non-contact form of transducer would be inefficient but much easier to homebrew (I assume quite tuneable and mode-controllable) and more familiar technologically to me as it would essentially just be a special kind of loop antenna. One crazy idea is super-regenerative detection using the same work coil; use a MCU to launch an RF pulse, then after quenching the oscillator re-enable it after a variable delay then measure how long it takes to build to a set amplitude, effectively sampling the returned signal at a particular instant. Calculations say it is at least possible, based on previously observed quench cycle times with RF oscillators. This is also a rather unique way of performing the temporal window ("sensitive instant") experiment I have long wished to attempt with super-regenerative receivers. While using an acoustic delay line in an RF experiment may sound a little crazy it is likely far more manageable than long coaxial transmission lines and strongly isolating gating switches.
Experiments with stretched wires would be interesting too, as tension could control transverse wave velocity and the complicating factors of physical extent with respect to wavelength; multipathing, dispersion, mode conversion, etc would be much less obvious or completely suppressed. It should be fairly easy to launch and detect vibrations from stretched wires too. Strong damping would be required I suspect as strings usually have quite impressive mechanical Q.
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