Question

ASSERTION: When a closed organ pipe vibrates, the pressure of the gas at the closed end remains constant.
REASON: In a stationary-wave system, displacement nodes are pressure antinodes, and displacement antinodes are pressure nodes.
(A) Assertion is True, Reason is True; Reason is a correct explanation for Assertion.
(B) Assertion is True, Reason is True; Reason is not a correct explanation for Assertion.
(C) Assertion is True, Reason is False.
(D) Assertion is False, Reason is True.

Answer 1

Hint: Nodes are points of no displacement or movement at the two fixed ends of the string. Closed end of an organ pipe is the displacement node. So, it must be a pressure antinode. Similarly, displacement antinodes are pressure nodes.

Complete answer:
These natural frequencies are known as the harmonics of the instrument; each harmonic is associated with a standing wave pattern.
A standing wave pattern is defined as a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source in such a manner those specific points along the medium appear to be standing still. In the case of stringed instruments, standing wave patterns depict the amount of movement of the string at various locations along its length.
Standing wave patterns show nodes. Nodes are points of no displacement or movement at the two fixed ends of the string.
There is a node at the closed end and an antinode at the open end. In the case of air columns, a closed end in a column of air is analogous to the fixed end on a vibrating string. That is, at the closed end of an air column, air is not free to undergo movement and thus is forced into assuming the nodal positions of the standing wave pattern. Conversely, air is free to undergo its back-and-forth longitudinal motion at the open end of an air column; and as such, the standing wave patterns will depict antinodes at the open ends of air columns. If the air is blown lightly at the open end of the closed organ pipe, then the air column vibrates (as shown in figure) in the fundamental mode.
In a stationary-wave system, displacement nodes are pressure antinodes, and displacement antinodes are pressure nodes. At the closed boundary there is a displacement node and pressure antinode, thus pressure varies at the closed boundary.
It can be said that assertion is false, while the reason is true.
Hence Option D is the correct option.

Note:
Reflection of sound waves from a rigid boundary (e.g. closed end of an organ pipe) as analogous to reflection of a string wave from rigid boundary; reflection accompanied by an inversion i.e. an abrupt phase change of pressure. This is consistent with the requirement that displacement amplitude remains zero at the rigid end, since a medium particle at the rigid end cannot vibrate.