METHOD:
A cct was bread boarded  as shown in the LHS figure with a 1K resistor  in series on GND side. The input signal, Vi, was supplied by an "Advance" AF signal generator. Sine waves were used for all measurements. the AF signals Vi & Vo were measured with an HP model 400H VTVM. The relationship between Vi, Vo and the variable impedance "Z" of the transducer is given by Eq. (1.0) This can be rearranged to yield Z when Vi, Vo & R are known as shown in Eq. (1.1). (R=1 kohm in this case) Signals of frequency from 50 Hz up to 50 kHz, the max the signal generator is capable of, were applied to the transducer. The results are tabulated below.

NOTE : The xtal is mounted on its metal acoustic plate in its enclosure. Measurement was done in air and not water.

RESULTS

Frequency, input & output voltages
freq, Hz	Vo, volts	Vi, volts	Vo+Vi	Vo/Vi	R*(Vi/Vo-1),  ohms
50	0.150	16.200	16.350	0.009	107000.0
80	0.230	16.000	16.230	0.014	68565.2
100	0.270	15.800	16.070	0.017	57518.5
150	0.380	15.300	15.680	0.025	39263.2
200	0.490	14.800	15.290	0.033	29204.1
300	0.670	13.700	14.370	0.049	19447.8
400	0.630	14.400	15.030	0.044	21857.1
800	0.880	11.500	12.380	0.077	12068.2
1000	0.920	8.500	9.420	0.108	8239.1
1500	1.040	6.500	7.540	0.160	5250.0
2000	1.050	5.300	6.350	0.198	4047.6
3000	1.100	3.700	4.800	0.297	2363.6
4000	1.100	2.800	3.900	0.393	1545.5
8000	1.100	2.100	3.200	0.524	909.1
16000	1.100	1.650	2.750	0.667	500.0
32000	1.100	1.500	2.600	0.733	363.6
50000	1.100	1.490	2.590	0.738	354.5

DISCUSSION
The crystal element behaves as a high pass filter, something which we knew already. Looks like its 3 dB frequency is around 2500 - 3000 Hz. This is way too high for our purposes : we want to construct a hydrophone/underwater sound projector  which will comfortably pass signals down to around 100 Hz. The vocalizations of land animals of which we have some experience have BWs of around 10 Hz to about 8 kHz. We don't know what to expect from marine animals of course.

We constructed a crystal based acoustic transducer because it was cheap and easy to do. But it's becoming clear that its overall response is not what we need. Possibly the next experiment should be to utilize a pot core inductor bonded to an aluminum plate as the active acoustic element?

You'd get a reflection from the bottom which should propagate in shallow water by bouncing between surface and bottom. You'd get complex phase relationships though and no reflections at all where you had a soft muddy bottom that could absorb sound waves. So the poor ol'manatee, talked about in the references below,  would still get run over by the barge in the mpeg.

IntelliCAD drawing of the in-phase waves and the anti-nodal lines generated by an out-of-phase virtual source positioned 1 wavelength below the surface

REFERENCES (Supplied by J. B.)
1/ American Scientist - (Home Page)  http://www.sigmaxi.org/amsci/amsci.html
2/ ASA 142nd Meeting Lay Language Papers - "Manatees, Masking, and Boats " :  http://www.sigmaxi.org/amsci/amsci.html