Answer the following questions about standing waves in an air column that is closed at one end and open at the other.
(i) Define a node and an antinode with respect to displacement in a standing wave.
(ii) Explain why the closed end of such an air column must always be a displacement node while the open end must always be a displacement antinode.
(iii) With the help of neat sketches, describe the first three modes of vibration possible for this pipe and clearly mark the positions of nodes and antinodes in each mode.