Using LTSpice I took a look at the voltages at a 6 dB/oct highpass with 2 kHz.
I would have liked to add the circuit file. But I am not used to Windows and I do not know how to perform. With Ltspice Getting Started Guide you have a very good entry into LTSpice.
Charging up:
The first plot shows how the voltage across one of the paired capacitors is rising.
After about 300 seconds both have a voltage of 9 volts.
After these 300 seconds there is a burst of 10 cycles at 3.5 kHz. The source has a voltage swing of +/- 18 Vpeak (12,7 Veff; 36 Vpp).
Going on I want to give you two automatically calculated examples which show other results some have discussed before.
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Peter