If the only information you have is the frequency - then the simple answer is you can't.  However given that you do know the frequency - then you can at least start to select which would be the most appropriate measurement tool to use to quantify the amplitude directly.  The two easiest amplitude quantities to determine are displacement (with something like a laser interferometer) and pressure (with something like a hydrophone).  Hydrophone measurements are relatively simple to make - do mail me if you require additional information

I agree it is impossible to know the amplitude from frequency because there are not related. This depend of many factor. The first one is to know if the external frecuency are close to the "resonance" ("minimun impedance"). If it is the case it is possible to compare two transducer from the quality factor Q, but it is not possible the amplitud. As the previous colleague says it is possible with laser interferometer and using hydrophone (but only some average values)

What type of transducer are you trying to measure?

A piezo electric ceramic disc transducer (PZT) (STEMiNC) with resonance frequency

of 1 MHz

You could model your system computationally by using a commercial Finite Element tool.

The most of those tools (Ansys, Comsol etc.) provide a possibility to apply time dependent excitation forces (harmonic, random etc.).

Even in case of a classical mass - spring - oscillator (linear system) it is not possible to make any quantitative statements regarding amplitude of vibration without any knowledge about transfer function or excitation forces and physical properties like masses and stiffnesses.

In case of classical mass - spring - oscillator (linear systems) excited harmonically you can make the following qualitative statements (based on known transfer function):

1. The Amplitude of vibration is linear in terms of amplitude of exciting forces

2. The Amplitude of vibration is nonlinear in terms of excitation frequencies

In case of nonlinear systems (we live in a nonlinear world) the first statement is not valid in general.

With best regards

Alexander

P. S.: An example:

https://www.comsol.com/paper/resonant-frequency-analysis-of-quartz-shear-oscillator-15211