What Determines a Transducer's operational frequency?

There are enormous numbers of transducers out there. It would be a long process just to catalogue how many operate in this frequency range. What kind of transducer are you referring to? Is it an actuator or a sensor? What physical property does it transduce?

Guessing there's a chance you're talking about a loudspeaker, but 'transducer' actually means pretty much any sensor or output device. It needs a lot more clarity. Also you're actual goal; what's it being used for?

For all transducers, physics and internal circuitry (if any) determines the operational frequency. For instance, some large transducers may have higher capacitance (due to dimensions) and take longer to charge to achieve a voltage, therefore that's a time or frequency impact. Other transducers may have mechanical resonances due to the physical construction, and it may be either desirable, or highly undesirable, to operate at those resonances; therefore there's again a frequency impact. Similar types of things apply to other types of transducers.

Humm transducer immediately brings to mind crystal or ceramic. Never thought transducer as speaker but you are correct it does apply. The frequency range is beyond the typical tweeter high end speaker.

I guess we need a bit more information.

I'm unsure of the purpose of your question. A transducer's operating frequency is designed by stiffness, thickness, mass, etc. So it is what it is designed to be.

If you are wanting a transducer for a specific frequency, you need to buy one designed for that frequency. If you drive it off frequency, it becomes less efficient. There are some kinds of electromagnetic transducers that can operate over a wider range of frequencies. 

What is it you are trying to do? Are you saying that you need it to work over a wide range from 10kHz to 30kHz? A tweeter, like the kind you put in a speaker, can handle a wide range but 30kHz is rather high. You may find that some piezo tweeters may be able to operate at those frequencies, but with odd directional patterns and possibly with dips in response at different frequencies.

I'm looking to send a signal, but I dont know the precise frequency.
So Im wondering if the frequency is a strict physical property from the construction of a piezo electric, or other sorts of transducers,
or a range of frequencies.

Please explain what you are trying to do with a bit more detail.

Do you have a signal in mind - what kind of information are you trying to send.

Do you have a transducer in mind - there are probably millions to choose from.

Most low cost ultrasonic air coupled piezo electric transducers are high Q resonant devices with a narrow bandwidth - they only work over a narrow frequency band. Different transducers are available for different frequencies. The lowest cost easily obtainable ones work at about 40kHz.

Moving coil loudspeakers are also air coupled transducers and small ones can manage maybe 500Hz to 20kHz  - which is a big frequency range but rarely used for other than audio signalling - like speech and music. (Larger speakers an work at low frequencies but struggle for the high end.).

MK

A range that varies widely upon transducer type and model.

I know there are a number of bright minds in our community that can offer solutions provided they are given the details. Describe in layman terms what you want to do. I'm confident you will get some responses, with less frustration, than the guess and by golly I got it right method.

its not like communication, its more like trying to resonate an object, and detect the resonating.
The reason Im not sure what the signal is exactly, is the material has natural variations that cause the resonate frequency to occur within a range of frequencies.