Similar circuits mostly use a condensor mic / preamp filtered by active feedback-loop type notch or narrow-bandpass filters, some with frequency band-pass tuning.
The key-finder keyring-fob is probably the audio-sensor part of what you need.
Except these use a monolithic I.C. covered by a black blob of epoxy - not traceable.
Drives an oscillator to return a 'beep' to a human whistle and most other KHz frequencies).
The commercial "hand-clap" switches work on the timing principle you need.
If you clap once, nothing happens. Clap twice within about 0.5 sec, and the circuit activates a relay.
I opened mine to see "what makes it tick".
My hand-drawn traced circuit unfortunately got damaged / discarded, but remember it used a c/mic then 741 op-amp as part of filter, to various logic IC's (forgot which since then). Switch now buried in storage..
A hand-clap is white/pink noise analyzed at fpeaks about 11.5-13 KHz.
Your CCT will likely fall into the lower audio range of about 500 - 5 KHz (My smartphone's peak is 2.2 KHz).
I'll dive into my old magazine-storage boxes, as I plan a very similar project to wirelessly extend top-loader 2-tone beep* from bathroom to lounge via mini FM tx. Then a relay / S.C.R / Triac for small lounge-mounted lamp.
*(Pre-rinse pause, waits for fabric-softener, beeping, then after 'X' seconds idle, continues "softener-less").
W/M alarm-tone beeps about** 1875 Hz, 2342 Hz, pause, repeat.
**From memory recall.