This problem involves the reflection of a longitudinal pressure wave (a sound pulse) at the end of a pipe. A high-pressure pulse is a compression. We need to analyze the reflection at two different types of boundaries: an open end and a closed end.

Step 1: Analyze Reflection at an Open End

1. Boundary Condition: An open end of a pipe is open to the atmosphere. The pressure at this end is always equal to the atmospheric pressure. Therefore, the excess pressure (the pressure variation from atmospheric) must be zero at an open end. An open end acts as a pressure node.
2. Physical Process: A high-pressure pulse (compression) travels down the pipe. When this compression reaches the open end, the compressed air is free to expand outwards into the open atmosphere.
3. Reflection: Due to inertia, the air rushes out and overshoots the equilibrium, causing a drop in pressure just inside the pipe's end. This creates a region of low pressure (a rarefaction). This rarefaction then propagates back up the pipe as the reflected pulse.
4. Conclusion: A high-pressure pulse reflects as a low-pressure pulse from an open end. This is equivalent to a phase change of $\pi$ (or 180°) for the pressure wave upon reflection.

• Option A: a high-pressure pulse starts travelling up the pipe, if the other end of the pipe is open. This is incorrect.
• Option B: a low-pressure pulse starts travelling up the pipe, it the other end of the pipe is open. This is correct.

Step 2: Analyze Reflection at a Closed End

1. Boundary Condition: A closed end is a rigid wall. The air molecules cannot move through the wall. Therefore, the displacement of air molecules at a closed end must be zero. A closed end acts as a displacement node.
2. Physical Process: When the high-pressure pulse (compression) reaches the rigid wall, the forward-moving air molecules are stopped abruptly. They pile up against the wall, causing the compression and thus the pressure to increase even further at the boundary.
3. Reflection: This region of maximum pressure then pushes back on the air column, creating a high-pressure pulse that travels back up the pipe.
4. Conclusion: A high-pressure pulse reflects as a high-pressure pulse from a closed end. There is no phase change for the pressure wave upon reflection at a rigid boundary.

• Option C: a low-pressure pulse starts travelling up the pipe, if the other end of the pipe is closed. This is incorrect.
• Option D: a high-pressure pulse starts travelling up the pipe, if the other end of the pipe is closed. This is correct.

Final Answer Summary

Based on the analysis:

• When the pipe end is open, a high-pressure pulse reflects as a low-pressure pulse (Option B).
• When the pipe end is closed, a high-pressure pulse reflects as a high-pressure pulse (Option D).

Both B and D are correct statements.