Two air columns of identical length L are studied in the laboratory. Column X is open at both ends, while column Y is closed at one end and open at the other.
Throughout this question, neglect end correction effects unless explicitly instructed otherwise.
(a) For the fundamental resonance of each column, describe the displacement pattern of the air molecules along the tube. In your description, identify the locations of nodes and antinodes relative to each end of the tube.
(b) Explain qualitatively why the set of possible resonant frequencies for column Y is different from that of column X, even though both columns have the same length.
(c) Using reasoning based on standing-wave patterns, determine the ratio of the first three resonant frequencies of column Y to the first three resonant frequencies of column X. Express each ratio in simplest integer form and justify your answer.