Free-end reflection

Let us assume the right end of the rope has a small loop, there is a bar standing vertically at the x-coordinate of 50, and the bar goes through the loop. When one grabs the left end of the rope, and send a pulse from left to right by snapping one’s hand. Then, the pulse is reflected at the right end and travels back to left. The next video shows this type of reflection, where the right end of the rope is at the x-coordinate of 50.

The right end of the rope can be move up and down freely, as the bar goes through the loop. Therefore, this end is called “free end.” The displacement of the free end reaches twice as high as the maximum displacement of the original pulse. In addition, when the pulse is reflected at the free end, the direction of the pulse is not inversed, so that the displacement of each dot is positive not only before also after the reflection. Please note that the tension force is only applied horizontally at the loop against the bar.

In fact, the video clip above is very similar to one below; the left half of the two videos are exactly the same.

The next video clip shows three cycles of a sinusoidal wave traveling from left to right. This wave is not inversed at the free end on the right. We can observe the original and the reflected waves are superimposed one on the other

The video clip above is also exactly the same as the left half of the one below.

So far, the animations were all about transverse waves. Now, let us take a look at the following videos of longitudinal waves with the free end reflection. In these videos, a multiple spring-mass system is applied.

The next video is the slow motion version.