How are ultrasonic bursts generated electronically?
The ultrasonic transducer can be modelled in terms of resistances, capacitances and inductance (RCL). 

Whenever you get RCL circuits you get resonance effects (the frequency it want to vibrate at) due to the LC part of the circuit. 

A pulse input momentarily moves the circuit away from its equilibrium position and the system will start to vibrate at its resonant frequency. Through each cycle some of the energy is lost and so the amplitude of vibration decreases with time. This is called damping. 

For comparison I've shown a simple mechanical system which exhibits the same properties.

Typically these systems exhibit the same shape of output graph with the sinusoidal resonant frequency output rising to a maximum and then decaying more slowly.