Name That Harmonic: Open-End Air Columns - Questions 6 Help

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If you blow across the top of a bottle, the air particles inside are set into vibrational motion. This is referred to as air column resonance. For a long cylindrical column, there are clear mathematical relationships associated with the standing wave pattern, the frequency, and the wavelength. This Concept Builder focuses on air columns in which both ends of the column are open to the surrounding atmosphere. These are called open-end air columns.

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Identify the standing wave pattern for an open-end air column that is vibrating with a sixth harmonic wave pattern.

When an air column resonates with one of its harmonic frequencies, a standing wave pattern is formed in the column. Such a pattern has nodes - points that don't move - and antinodes - points that vibrate wildly. The antinodes are located at the open ends. A node is located between every antinode. There are a number of standing wave patterns that could form. In this question, you must identify the pattern associated with the sixth harmonic.

The standing wave pattern for the first harmonic or fundamental frequency displays the longest possible wavelength of all the harmonics. Given the rule that there are vibrational antinodes at each of the open-ends, the longest wavelength would have these two antinodes and a single node in the middle. Each successive harmonic after the first harmonic would have an additional node and antinode. So the second harmonic would have two nodes and three antinodes. The third harmonic would have three nodes and four antinodes. And so forth. So you need to tap through the choices until you find the harmonic that has six nodes between its ends.

Try this link to The Physics Classroom Tutorial for more help with the concept of standing wave patterns in open-end air columns:

Open-End Air Columns