Right; it's probably because I'm not enlightened, but the correct answer just seems to be a password. My intuition is that if you properly carved reality at its joints then 'clap' would not make sense in this context; it'd be a meaningless question.
The most benevolent scenario I can come up with is that the Chinese word that was in the place of "clapping" doesn't map 1:1 to English "to clap", and that there was, if not wisdom, at least some wit in the subset of its meaning that was left behind.
The first time I heard this question, when I was a small child, I immediately started clapping my right hand's fingers against my palm. It sounds like normal clapping but quieter and a little bit more high-pitched. "What's the big philosophical mystery?", I thought.
IIRC, the original form of the koan is "You have heard the sound of two hands clapping. What is the sound of one hand?" This is a bit more ambiguous.
V whfg pync zl svatref ntnvafg gur cnyz bs zl unaq, vg znxrf na npprcgnoyr pynccvat fbhaq (Guvf qbrfa'g pbzr sebz tbbtyr). Fb gur nafjre jbhyq or "n pync, ohg abg n irel ybhq bar".
The other most famous zen koan, has a distinct and correct answer that is not mu. In the same way that the answer to "what is the sound of two hands clapping?" is to perform an action, the answer to this koan is an action. While there is an endless amount of deconstruction that you can do once you have the answer, the correct answer itself is not deconstruction, but a simple answer.
I'm surprised at how rare knowledge of the answer of this koan is when it's easy to find the answer by Googling "what is the sound of one hand clapping?". I wonder why the answer to the mu koan seems to be so much more widespread than the answer to this koan, when the one hand clapping koan is even more popular in the West than the mu koan. Please don't post answers that come from Google in this thread without spoiler warnings.