Final answer:
The distance from one node to the next in a standing wave is always half a wavelength, as nodes represent points of destructive interference that occur at fixed intervals along the wave.
Step-by-step explanation:
The distance from one node to the next in a standing wave is indeed always half a wavelength. This is because a node is a point of no displacement caused by the destructive interference between two waves traveling in opposite directions, and the distance between successive nodes, or two points of destructive interference, corresponds to one-half of the wave's full cycle or wavelength.
In situations such as when dealing with standing waves created in musical instruments or other physical systems, it's essential to recognize that the nodes occur at fixed points in space where the two waves cancel out each other. The antinodes, conversely, are points of maximum displacement and occur midway between the nodes. As such, the distance between a node and an adjacent antinode is one-fourth of a wavelength.
Understanding the relationship between node distance and wavelength is crucial in applications like calculating the modes of vibration in strings or air columns and analyzing patterns of interference in light and other wave phenomena.