A

In a stationary wave, also known as a standing wave, certain characteristics define the behavior of the particles in the wave.

Step 1: Understand the structure of stationary waves. A stationary wave is formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions.

Step 2: Identify nodes and antinodes. In a stationary wave, there are fixed points called nodes where the particles do not move. Between these nodes are antinodes, where the maximum amplitude of oscillation occurs.

Step 3: Analyze particle movement. During each complete cycle (one period of oscillation), all particles at the nodes remain at rest, and this occurs twice in that period: once when they are at the lowest point of the waveform and again when they return to that lowest point.

Step 4: Conclusion. Thus, in a stationary wave, all particles are at rest at the same time twice during each complete oscillation. Hence, the correct statement is represented in Option A.