Appendix B: How is Sound Wave Reflected by an Open End? (Beyond the Syllabus)

Finally, let’s address the elephant in the room: why is a sound wave reflected even by an open end?

Most textbooks skim over this question with little explanation. After combining the insights from various sources, and filling in the missing details in their explanations, I have formed my own idea on the matter, which I will share below. Here we go.

I imagine the air in the pipe to be a human chain, like a slinky made up of people instead of loops.

Compression propagating rightward meets a Closed End

Suppose the 1st person on the left loses his balance and falls rightward. He will push the 2nd person rightward and regain his balance. But the 2nd person has now lost his balance and falls rightward… So we have started a compression propagating down the line. The last person will be pushing a wall. In pushing the immovable wall rightward, he “overcorrects” and falls leftward instead. Now he will be pushing the 2nd last person on his left to regain his balance. In so doing, he triggers a compression leftward. So a compression is returned as a compression.

Rarefaction propagating rightward meets a Closed End

Now let’s try rarefaction. Suppose the 1st person on the left loses his balance and falls leftward. He will pull the 2nd person leftward to regain his balance. But the 2nd person has now lost his balance and falls leftward… So we have started a rarefaction propagating down the line. The last person will be pulling a wall (or perhaps a handle fixed on the wall). In pulling the immovable wall leftward, he “overcorrects” and falls rightward instead. Now he is pulling the 2nd last person on his left rightward to regain his balance. In so doing, he triggers a rarefaction leftward. So a rarefaction is returned as a rarefaction.

Now suppose the right end is not a wall but empty air.

Compression propagating rightward meets an Open End

When a compression reaches the end, the last person will be pushing air rightward. Obviously, air does nothing to slow him down. He “overshoots” and continues to fall rightward and is now pulling the 2nd last person on his left rightward to regain his balance. In so doing, he triggers a rarefaction leftward. So a compression is returned as a rarefaction.

Rarefaction propagating rightward meets an Open End

Similarly, when a rarefaction reaches the end, the last person will be pulling air leftward. Obviously, air does nothing to arrest his leftward momentum. He continues to fall leftward and now pushes the 2nd last person on his left leftward to regain his balance. In so doing, he triggers a compression leftward. So a rarefaction is returned as a compression.

Animation

Music Acoustic at UNSW

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