Understanding Standing Wave Diagrams 1 - Both Ends Fixed

Standing waves are usually shown on a printed page as a static, or motionless, diagram. Of course, like all waves, they are dynamic; they have a motion. This interactive animation will help you understand how a static standing wave diagram is meant to convey the true motions of the standing wave.

To understand how to use this app do the following:

• Check the '1st' harmonic radio button.
• Check the 'Wave' checkbox, uncheck the 'Envelope' checkbox. You will see a moving yellow string. What you are looking at is the true motion of a string fixed at both ends and vibrating in its fundamental mode, or its first harmonic. Of course, static diagrams could not show this motion. Take note of the maximum extents of the string's motion.
• Now uncheck the 'Wave' checkbox and check the 'Envelope' checkbox. What you are looking at now is a shape that outlines the maximum of the string's motion. This outline is called the envelope of the vibration. Static diagrams of standing waves usually only show this envelope.
• Now check both the 'Wave' and the 'Envelope' checkbox. You will be able to see both the wave motion and the static envelope diagram.
• Try all of this with the other harmonics.

Again, a static diagram representing a standing wave will usually only show the envelope of the vibration.

Below are several static diagrams of standing waves for a medium fixed at both ends, along with the names for each vibration and a count of the antinodes and nodes for each vibration.

If you are unclear about the meaning of the terms 'antinode' and 'node', be sure to look back at Understanding Standing Wave Diagrams. Page through the animation which you will find there. The meaning of the terms 'antinode' and 'node' is presented in that animation and also in the discussion on that page.

Picture of Standing Wave	Name	Structure
	1st Harmonic or Fundamental	1 Antinode 2 Nodes
	2nd Harmonic or 1st Overtone	2 Antinodes 3 Nodes
	3rd Harmonic or 2nd Overtone	3 Antinodes 4 Nodes
	4th Harmonic or 3rd Overtone	4 Antinodes 5 Nodes
	5th Harmonic or 4th Overtone	5 Antinodes 6 Nodes

Notice that this harmonic structure is the same as that for the medium open at both ends, but different from that for the medium fixed at one end and open at the other end. This harmonic structure, like the one for both ends open, proceeds from the 1st to the 2nd to the 3rd harmonic, and so on. The harmonic structure for the fixed at one end and open at the other end medium proceeds from the 1st to the 3rd to the 5th harmonic, and so on.

However, in every case, (fixed at both ends, open at both ends, fixed at one end and open at the other end), the first possible standing wave is called the fundamental, the second possible standing wave is called the 1st overtone, the third possible standing wave is called the 2nd overtone, and so on.