How do standing waves form inside a tube?

Standing waves form inside a tube when two identical sound waves travel in opposite directions and interfere with one another. This process occurs because the waves are confined to the tube, causing them to reflect off the ends and produce a series of waves that interfere constructively and destructively.1

The specific behavior of these waves depends on the tube's boundary conditions:

• Open Tubes: Both ends allow air motion, resulting in a velocity or displacement antinode at each end. The fundamental mode has antinodes at both ends and a node in the center, making the tube one-half wavelength long.14
• Closed Tubes: The closed end prevents air movement, creating a velocity node, while the open end remains an antinode. Consequently, the tube length is one-quarter of a wavelength, and only odd harmonics are supported.12

In both cases, the resulting standing wave consists of fixed nodes (zero displacement) and antinodes (maximum displacement) spaced at regular intervals.13