A Zen koan primarily associated with Hakuin Ekaku zenji, the Japanese Tokugawa era revitalizer of Rinzai Zen. The phrase "the sound of one hand" does not involve clapping or anything of that nature. In its correct form, it is simply, "What is the sound of one hand?" This means, what does this hand, this eye, this foot, this breath, tell you about who and what you are? The phrase did not originate with Hakuin but was popularized by him and used as one of the miscellaneous koan practised before the Gateless Gate, the Blue Cliff Records series and so on.

An early (Song dynasty) occurence of the phrase is in Case 18 of the Blue Cliff Records, as follows:

Case 18: Huizhong’s Seamless Stupa

The Koan:

Emperor Suzong asked National Teacher Huizhong, “After you die, what shall I do to honour you?”

The National Teacher answered, “Build this old monk a seamless stupa.”

The emperor said, “Master, please tell me what style to build it in?”

The National Teacher was silent for a long time and then he said, “Do you understand?”

The emperor said, “I don’t understand.”

The National Teacher said, “I have a disciple who has received my Transmission, Danyuan. He is well versed in this matter. Go to him and ask him.”

After the National Teacher’s death, the emperor summoned Danyuan and asked him about it.

Danyuan said,
“South of Xiang and north of Dan,
(Xuedou says, “Soundless sound of one hand.”)
in between, the gold of the nation.
(Xuedou says, “A mountain monk’s staff.”)
A ferryboat under the shadowless tree.
(Xuedou says, “Calm seas, clear rivers.”)
In the jewelled palace, no one knows.”
(Xuedou says, “That’s it.”)

translated by Yasuda Joshu Dainen roshi and Anzan Hoshin roshi; used with permission