A pipe has one end open and the one end closed. Where must the node be located in order for a standing wave to occur? (The left end, B, is the open one and the right end, A, is the closed one.)
The antinode is at the open end, the node at the closed end.
Are there any times when the node could be in the middle and not at either of the ends?
yes, but at each harmoic, there will be one node at the closed end, and an antinode at the open.
To determine where the node must be located in order for a standing wave to occur in a pipe with one end closed and one end open, we need to understand the properties of standing waves.
A standing wave is formed by the interference of a wave traveling in one direction and a reflected wave traveling in the opposite direction. In the case of a pipe with one end closed and one end open, the closed end reflects the wave, while the open end allows the wave to escape.
In a standing wave pattern, nodes are points of complete destructive interference, where the displacement of the wave is always zero. Antinodes, on the other hand, are points of complete constructive interference, where the displacement of the wave is at its maximum.
For a pipe with one end closed and one end open, the node must be located at the closed end (A), as a node represents the point of zero displacement. At the closed end, the reflected wave interferes with the incident wave with complete destructive interference, resulting in a node. At the open end (B), there will be an antinode since the incident wave and reflected wave constructively interfere.
So, in summary, the node must be located at the closed end (A) of the pipe in order for a standing wave to occur.