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Among many species, applause was a sign of respect and approval. The act of applause was also known as "clapping".
Bajorans and Wadi applauded by clapping the back of one hand into the palm of the other. Cardassian applause was generated by tapping a table or armrest with a clenched fist. (DS9: "Move Along Home", "In the Cards", "Tribunal", "Sons and Daughters")
For Humans, applause was performed by clapping both palms together. This method was also used by non-Human Starfleet officers, and others within the Federation. In 2376, it was copied by the Qomar, who used it in appreciation of musical performances. (VOY: "Virtuoso")