Reflection of High Pressure Air Pulse from Open and Closed Ends of Pipe

To determine the nature of the reflected pulse, we analyze the reflection of acoustic pressure waves at open and closed boundaries of a pipe.

1. Physics of Sound Wave Reflection

A high-pressure pulse corresponds to a compression pulse where the local pressure variation is positive ($\Delta P > 0$).

• Reflection at an Open End: An open end of a pipe communicates directly with the surrounding atmosphere, maintaining the acoustic pressure at a constant atmospheric value. Thus, an open end acts as a pressure node (fixed boundary for pressure waves).

  To satisfy the condition $\Delta P_{\text{net}} = 0$ at the open boundary, the reflected pressure wave undergoes a phase shift of $\pi$ radians ($180^\circ$): $\Delta P_{\text{reflected}} = -\Delta P_{\text{incident}}$ Since the incident pulse is a high-pressure pulse ($\Delta P_{\text{incident}} > 0$), the reflected pulse is a low-pressure pulse ($\Delta P_{\text{reflected}} < 0$, i.e., a rarefaction).

  Therefore, a low-pressure pulse reflects back if the far end is open.

• Reflection at a Closed End: A closed end of a pipe restricts the displacement of air molecules to zero, acting as a displacement node. Correspondingly, it behaves as a pressure antinode (free boundary for pressure waves).

  At a free boundary for pressure waves, the reflected wave undergoes no phase shift ($\Delta \phi = 0$): $\Delta P_{\text{reflected}} = \Delta P_{\text{incident}}$ Since the incident pulse is a high-pressure pulse ($\Delta P_{\text{incident}} > 0$), the reflected pulse remains a high-pressure pulse ($\Delta P_{\text{reflected}} > 0$, i.e., a compression).

  Therefore, a high-pressure pulse reflects back if the far end is closed.

Conclusion

• Statement (B) is correct.
• Statement (D) is correct.

Correct Options: (B) and (D)