10.7.1 Wave Reflections

So, a standing wave is formed by superposing two identical waves (same frequency, same amplitude) travelling into each other. You may be wondering, what’s the chance of such a thing happening? Actually, it is a common occurrence. Thanks to reflection.

Imagine that a pulse is sent scrambling towards the end of the slinky. When it reaches the fixed end, it has nowhere to go but return.

Now, what if instead of a fixed end, we have a loose end? Does the pulse disappear into thin air when it reaches the loose end? Surprise! Whether the end is fixed or loose, the pulse always returns.

But there is a difference in the way the pulses return. With the fixed end, the pulse returns on the opposite side. If you want to sound like an expert, you can say “oh, the pulse underwent a phase change of 180°”. With the loose end, the pulse returns on the same side. You can say, “Ooh, this reflection did not incur any phase change.”

What if instead of a pulse, we have a continuous sine wave? When the wave arrives at the end (fixed or loose), it undergoes reflection and returns. Voila, the incident wave superposes with the reflected wave to form a perfect standing wave!

If the end is a fixed end, a 180° phase change occurs at the reflection. The incident and reflected waves[1] superpose to form a standing wave with a node at the fixed end.

If the end is a loose end, no phase change occurs at the reflection. The incident and reflected waves superpose to form a standing wave with an antinode at the loose end.

Demonstration

Slinky Fixed and Loose End

Applet

Walter Fendt (Reflected Wave)

Concept Test

2053


[1] To draw a reflected wave, just flip it horizontally (i.e. with a vertical mirror line) at the reflection point. If there is a 180° phase change, do an additional vertical flip (i.e. mirror it about the horizontal axis).

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