Need this waveform. How to generate it?

[amgen]

that looks like the ringing of the inductor by a single pulse of say a few milliseconds ??

[kellyseye]

Many piezo devices are available that have 110dB+ outputs but users seldom drive them according to the manufacturers spec, particularly the correct 'resonant' frequency they are designed to run at. Find a suitable piezo (voltage range) and output (dB) and use it according to the specifications and it will be loud enough!
All that the circuit does that you have posted is rely on the resonant frequency of the L/piezo (effectively a parallel tuned crystal circuit) which is being 'rung' by the applied waveform - much like ringing a bell.

[Pista1]

Piezo speakers have a high impedance hence they require a relative higher driver Voltage. 2 AAA batteries may supply about 1V RMS at best. That is why you need a step up transformer which in your case happens to be an autotransformer. The primary coil is A-C, the secondary coil is B-C. Since this is an auto transformer the secondary coil includes the primary coil in series, as a result the primary Voltage adds to the secondary Voltage.
The number of turns is directly proportional to the Voltage across the coil. For instance if the primary coil is 3 turns and the secondary coil is 30 turns you will get in case of 1 V RMS input 10+1 Volts = 11 Volts RMS.
Of course the previously mentioned posts about the ringing and self resonant of the Piezo element are all true.

[Megahertz]

Thanks for the answers. I am trying to find a autotransformer but I cannot find any which resembles this component, the search on google always shows auto-transformers for mains. Is there any other term as well for this?
I also checked the peak voltage when this components operates and it gives around 25v amplitude to the piezo which is very close what the max limit of this piezo is (30vpk), so everything said above makes perfect sense.

From more checks, primary side has 106R & secondary side has 2R resistance.
At 3.5Khz I literally went deaf for few seconds