C

Step 1: Understand the nature of stationary waves. A stationary wave, also known as a standing wave, is a wave that remains in a constant position. It is formed by the interference of two waves of the same frequency and amplitude traveling in opposite directions.
Step 2: Analyze why stationary waves don’t transmit energy. In a stationary wave, energy is not transmitted along the wave itself; instead, energy is stored in the wave pattern created by the interference.
Step 3: Review the options:

• Option A: Incorrect, as particles do oscillate, only they do not propagate energy.
• Option B: Incorrect, as particles undergo SHM but remain in fixed positions.
• Option C: Correct, as there is no net energy flow in a stationary wave.
• Option D: Incorrect, interference is fundamental to the creation of stationary waves.

Therefore, the correct answer is C.