I don't know what medium you are using, but assume it is liquid or much lower impedanc than air.
Impedance matching is critical on linear interfaces to avoid false echoes. If the ESR of your transducer does not match the ESR of the medium, then mechanical horns can amplify the pressure wave and transform the impedance by gain-squared to help in matching. Although cavitation may occur from excess power density at the interface and thus abrupt impedance rise, the impedance is largely newtonian mass vs pressure @f with the fluidic dampening like capacitance.
To answer your question, I dont have the impulse response or burst F envelope response to determine your situation, but usually, mismatch at the exciter<>medium interface is always mismatched, so interface echoes will always exist which causes reflected current you do not want. By having a very low driver impedance, this echo current during Tx gets attenuated. Since the medium velocity of pressure is far lower than the electrical velocity at 2/3c , the electrical mismatch is less important than suppressing the mechanical interface echo. Thus you want an ideal voltage source, e.g. negative feedback source with gain reduced Impedance to suppress the mechanical echoes at the interface. Thus is why it is done with a dampening factor of load/source=100 to 1000 in high power woofers. Higher= better. Although you do not get maximum power transfer like in linear telephones, RF and microwave linear devices, you get minimum mechanical echo and distortion.
Your objective is to make the best impedance match at the interface of the sensor. Rigid mount, with horn, then lowest impedance on source to suppress interface reflections.
Impedance matching is normally done reactive loads using the complex conjugate.
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