For a standing wave formed within an open ended air column, which of the following statements describe the condition at both ends?

Question

BlackTom AI · Accepted Answer

The question asks about the boundary conditions at the ends of an open-ended air column when a standing wave is formed.
Option a: 'A pressure node and displacement node is formed' would imply both pressure and displacement vanish at the ends, which is not true for an open end. At an open end, the air is free to move, so the pressure variation is zero (node) but the displacement variation is maximum (antinode).
Option b: 'A pressure antinode and displacement antinode is formed' suggests both pressure and displacement are at maximum at the ends. In an open-ended tube, the pressure is not maximized there; instead, the pressure variation is zero, so a pressure antinode is incorrect.
Option c: 'A pressure node and displacement antinode is formed' correctly identifies the boundary conditions for an open end: the pressure variation goes to zero (pressure node) while the particle displacement is maximal (displacement antinode). This aligns with the standard open-end standing-wave pattern where air can move freely, enforcing zero pressure fluctuation but maximum displacement at the ends.
Option d: 'A pressure antinode and displacement node is formed' would indicate a high-pressure variation and zero displacement at the ends, which contradicts the physical reality of an open boundary where the air is not confined and can move, so displacement is not suppressed.
Overall, the only option that matches the physical boundary conditions for an open-ended air column is option c, reflecting the correct combination of a pressure node and displacement antinode at the ends.

For a standing wave formed within an open ended air column, which of the following statements describe the condition at both ends?

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