There are distance measurement devices commercially available, but if none will do, then I recommend making your own using a pulsed laser, a detector, and accompanying electronics.
Another method would be a small buoy with a radio transmitter and a sound generator inside. The radio transmitter sends a signal once per minute and the sound generator emits a sound at the same time. The time difference between the radio signal detected and the sound signal detected, can be used to give the distance from the buoy to the detectors (water depth).
To measure the response of your material you need to more clearly define what your input (excitation), and your output signals are going to be. If you decide your input is voltage then your choices for the output are probably limited to either current or displacement. Frequency is neither an input nor an output, but rather a property of the signals being applied or measured. And if I understand your question you want to know the response at a particular frequency, the resonant frequency.
But piezoelectric materials will typically have multiple resonant frequencies and different resonant frequencies in different directions depending on the electrical properties of the material, but also its geometry. So what you really need to do, as suggested by CuriousOne, is determine the frequency response over a range of frequency. This can be done by applying either a swept sine, also known to academics as step sine, or broadband noise, and measure either the current or displacement. From captured time records you can calculate the one sided input auto spectrum, and the input-output cross spectrum. The ratio of the cross spectrum to the input autospectrum provides you with the complex frequency response function or FRF. From the FRF you can calculate magnitude and phase. The magnitude provides the gain factor you are looking for, and it will show you all the resonant peaks across the range of frequency you measured.
While such measurements and calculations can be done using simple data acquisition hardware and software such as MatLab, an easier, quicker way to measure your transducer is to use a Dynamic Signal Analyzer or DSA. The DSA does all the measurements and signal processing automatically, and provides you with another calculation to validate your measurement - the coherence function.
I've used DSA's to measure piezo material response in actuators and transducers, and in my opinion, it's the best way.
Best Answer
Most practical piezoelectric elements in use today are piezoceramics and the physics of these materials have been carefully studied, modeled and engineered to predict how they will behave for use as either sensors or actuators; transducers in general.
American PiezoCeramics (APC) has been thoughtful enough to post on their website a summary modes of piezoceramics elements. If you link to that page you'll see that indeed there are multiple modes to consider that depend on the shape and dimensions of the element as well as the particular material.
The frequency you are seeing is probably a mode (resonance) being excited across another dimension in the element. You should be able to use the chart to explain the 6kHz. If I recall there are 'tricks' you can employ like mounting the element in epoxy that can isolate the specific mode you are trying to excite and attenuate others.