Assertion (A) : A man standing on a completely frictionless surface can propel himself by whistling. Reason (R) : If no external force acts on a system, its momentum cannot change.

Assertion is true: a person can produce a recoil by whistling because the act typically involves accelerating and ejecting a small jet of air which carries momentum; the expelled air’s momentum produces a reaction force on the person. The Reason statement is also true as a general law: if no external force acts on a closed system, its total momentum is conserved [1]. However R is not the correct explanation of A as stated, because the man alone is not an isolated system — momentum lost by the man is carried away by the ejected air and/or outgoing acoustic radiation. Pure acoustic oscillations involve back-and-forth particle motion with negligible net mass transport, so alone they would not produce sustained recoil [2].

Sources

1. [1] https://www.physics.usyd.edu.au/~helenj/Mechanics/PDF/mechanics13.pdf
2. [2] https://ccrma.stanford.edu/~jay/subpages/Lectures/Lecture1-Acoustics.pdf