Free End Reflections Simulation

QUIZ

Q) When a wave pulse crosses the boundary from a fast medium into a slow medium

A. Both the transmitted and the reflected wave pulse are on the same side of the medium rest position
B. Both the transmitted and the reflected wave pulse are on the opposite side of the medium rest position
C. The transmitted wave pulse is on the same side, but the reflected wave pulse is on the opposite side
D. The reflected wave pulse is on the same side, but the transmitted wave pulse is on the opposite side

The transmitted wave pulse is on the same side, but the reflected wave pulse is on the opposite side

Free End Reflections Simulation

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Reflection
In our discussion of waves so far, we have assumed that the waves being analyzed could travel indefinitely without striking anything that would stop them or otherwise change their motion. But what happens to the motion of a wave when it reaches a boundary?

At a free boundary, waves are reflected
Consider a pulse wave traveling on a stretched rope whose end forms a ring around a post, as shown in Figure 01. We will assume that the ring is free to slide along the post without friction.
As the pulse travels to the right, each point of the rope moves up once and then back down. When the pulse reaches the boundary, the rope is free to move up as usual, and it pulls the ring up with it. Then, the ring is pulled back down by the tension in the rope. The movement of the rope at the post is similar to the movement that would result if someone were to whip the rope upward to send a pulse to the left, which would cause a pulse to travel back along the rope to the left. This is called reflection. Note that the reflected pulse is upright and has the same amplitude as the incident pulse.

Figure 01. When a wave in one medium (for example, string) encounters a medium with a lower density (for example, air), the wave is reflected with the same orientation and amplitude as the original pulse.

Media Boundaries: Amplitudes
The amplitude of a wave before it encounters a media boundary is closely related to the wave’s energy. The amplitude does not change if the wave’s energy remains constant.
When a wave encounters a media boundary that is not strictly an ideal free-end or fixed-end boundary, the wave splits into two. One wave is reflected, and the other is transmitted. The term transmission describes the process of a wave moving through a medium or moving from one medium into another medium. The amplitude of the original wave may not be shared equally by the reflected wave and the transmitted wave. However, the sum of the two amplitudes must equal the amplitude of the original wave (Figure 02).

Figure 02. At a media boundary that is neither free-end nor fixed-end, the original wave splits into two waves. (a) If the wave moving along the rope encounters a medium that has a slower wave speed, then the wave splits into two, and one wave is reflected and the other is transmitted. The reflected wave is upright. (b) When a wave moves into a faster medium, then the wave splits into two, and one wave is reflected and the other is transmitted. The reflected wave is inverted.

If the difference between the wave speeds in the two media is small, transmission is preferred—the amplitude of the transmitted wave is closer to the amplitude of the original wave. As a result, the amplitude of the reflected wave is much smaller because of the conservation of energy. For cases in which the wave speed is significantly different between the two media, reflection is preferred—the amplitude of the reflected wave is closer to the amplitude of the original wave.