The frequency for your ultrasonic transducer is not arbitrary. It (more or less) reflects the frequency for the highest amplitude of oscillation, assuming you are analyzing a resonance operated device.

 But why do we different devices have different frequencies frequencies? Isn't ultrasonic just ultrasonic?

 Why not make all ultrasonic devices at 20kHz? I'll quickly address two reasons:

1. [Space constraint] Because we need a device to be small, we are naturally constrained to work with higher frequencies. This is because frequency is inverse to size (sound bounces around more "frequently" in a smaller geometry)
2. [The desired effect requires a certain frequency] High frequency sound has shorter wavelengths, which is critical to consider for diagnostic ultrasonic applications. Lower frequency transducer (eg 20kHz) are able to transfer a large amount of energy, so that becomes the premium choice for welding applications