Sound waves in tubes, such as open-ended or closed-ended tubes, can exhibit a phenomenon known as standing waves. A standing wave occurs when a wave interferes with its own reflection, resulting in a pattern of nodes (points of minimal displacement) and antinodes (points of maximum displacement) that appear to be "standing still."
In a tube, the sound wave reflects back and forth between the ends of the tube. This reflection leads to constructive and destructive interference between the incident and reflected waves, creating regions of reinforcement and cancellation.
In an open-ended tube, such as an open pipe or the human vocal tract, the open end allows the sound wave to undergo a 180-degree phase shift upon reflection. This means that an incident wave with a peak (compression) at the open end will be reflected as a wave with a trough (rarefaction), and vice versa. This phase shift creates a standing wave pattern with an antinode at the open end and a node at the closed end (if the other end is closed).
In a closed-ended tube, such as a closed pipe or the end of a flute, the closed end does not allow air particles to vibrate, resulting in a node at the closed end. The open end, on the other hand, exhibits an antinode. This configuration also leads to the formation of a standing wave pattern.
The specific frequencies at which standing waves occur in tubes are determined by the length of the tube and the wavelength of the sound wave. These frequencies are called the resonant frequencies or harmonics of the tube. The lowest resonant frequency, known as the fundamental frequency or first harmonic, corresponds to the longest possible wavelength that fits in the tube. Subsequent resonant frequencies correspond to shorter wavelengths and higher harmonics.
Due to the fixed length of the tube and the specific interference patterns that arise, sound waves in tubes exhibit standing wave patterns, resulting in distinct nodes and antinodes. This characteristic makes them particularly interesting for the study of acoustics and musical instruments.