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In my extensive toilet-plunging experience, the best technique for plunging varies between clogs:
sometimes it's high amplitude and low frequency, sometimes it's high frequency and low amplitude, and
sometimes it's simply maximum power (something like the product of amplitude and frequency). It is
difficult to tell what the best technique will be without trying all of them, and sometimes it changes as
the clog shifts.
This device consists of a skirt that seals firmly to the toilet bowl, as in my thermite rocket plunger idea
, with a specially-designed high-displacement loudspeaker in the middle. This loudspeaker is used to
create rapid and drastic changes in the air pressure in the bowl, which, having nowhere else to go (the
holes leading the tank being sealed by the skirt), are transmitted to the water and from there to the clog.
Feedback, via either back-EMF in the loudspeaker or a separate pressure sensor having low response time,
is used to optimize the frequency and amplitude to break up the clog as efficiently as possible. Machine
learning can be used to implement this.
In the middle of the loudspeaker could be a socket for attaching a shortened traditional plunger (or my jet
plunger ) for more focused automatic plunging, if the bowl is not too full with toilet paper.
The skirt could optionally integrate my sonar toilet clog analysis idea  for even better feedback and
optimization. If not, the devices could be separate but connectable via cable or wireless link.
||// specially-designed high-displacement loudspeaker //
||But what to play? Industrial, metal or simply the Stones?
Would there be a clog-moving playlist and an iPod hookup?
||Definitely some concerns about the resonant frequency of various parts of the toilet.
||Nuclear plunger: A nuclear bomb for use in clearing plugged toilets.