10.8.2 Pressure Wave Reflections

Let’s recall that sound is a longitudinal wave, where the longitudinal oscillation of air particles produces regions of compression and rarefaction. Imagine a compression pulse propagating along a narrow pipe. When it reaches the closed end of the pipe, it must undergo reflection.

The same thing happens if it were a rarefaction pulse.

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

But there is a difference in the way the pulses return. With the open end, the compression pulse is reflected as a rarefaction pulse, and vice versa. In other words, the pressure wave undergoes a phase change of 180° at the open end. (Read Appendix 10.B if you’re interested to know why.)

What if instead of a pulse, we have a continuous sine wave?

In terms of pressure

If the end is a closed end, no phase change occurs during the reflection. The incident and reflected pressure waves[1] superpose to form a standing wave with a pressure antinode at the closed end.

If the end is an open end, a 180° phase change occurs at the reflection. The incident and reflected pressure waves superpose to form a standing wave with a pressure node at the open end.

In a way, it is only logical that the open end is a pressure node. The open end is basically directly connected to the atmosphere. Any pressure imbalance at the mouth of the tube will cause the outside air to either move towards or away from the mouth of the tube, thus maintaining the pressure at atmospheric pressure.

In terms of displacement

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

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

In a way, as far as displacement is concerned, a closed end is analogous to the fixed end of a string. Since air particles are not able to displace into a closed end, the closed end must be a displacement node (and hence pressure antinode). Likewise, an open end in a pipe is analogous to the loose end of a string. Since an open end allows air particles to displace in and out of the pipe, it must be a displacement antinode (and hence pressure node).

Animation

Music Acoustic at UNSW

Concept Test

2055


[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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