# Standing waves due to reflection

When the left end of a rope is in simple harmonic motion and the right end of the rope is fixed, a sinusoidal wave travels from left to right and the reflected wave travels from right to left after reflection (the fixed-end reflection). The next video clip shows these two waves are superimposed one on the other. In this video, the fixed-end is located at the x-coordinate of 50, and we assume there will be no reflection at the left end.

When watching this video above, we can observe a “standing wave,” which does not travel left or right. At the fixed-end on the right, the displacement of the red dot is always 0. In addition, all of the red dots does not move and their displacements are always 0. They are called “nodes.” In between the nodes, there are the middle parts where their displacements take the maximum and the minimum values. They are called “antinodes.” The maximum displacement of the standing wave is twice as large as the original amplitude of the sinusoidal wave produced by the simple harmonic motion. The wavelength of the original sinusoidal wave is the equivalent to the two loops of the standing wave.

When the left end of the rope is in simple harmonic motion and the right end of the rope is free, a sinusoidal wave travels from left to right and the reflected wave also travels from right to left after reflection (the free-end reflection). The next video clip shows these two waves are superimposed one on the other. In this video, the free-end is located at the x-coordinate of 50, and we assume there will be no reflection at the left end.

When watching this video above, we can, again, observe a “standing wave,” which does not travel left or right. In this case, the free-end on the right becomes the antinode, and all of the red dots become the nodes. In addition, each middle part of two adjacent red dots becomes the node.