All AP Physics 1 Resources
Example Questions
Example Question #11 : Harmonics And Standing Waves
Suppose that a pipe open at one end supports a wave whose wavelength is . If this wave is on its third harmonic, how long is the pipe?
To answer this question, we need to understand the concept of standing waves. A standing wave is a wave that exhibits both nodes and antinodes. A node is a fixed position where there is no displacement from the wave, and an antinode is a point of maximum displacement of the wave.
A standing wave can result from two individual waves traveling in opposite directions and interfering with each other. For instance, when a wave traveling through one medium (such as the air in the pipe) hits an interface that is denser (such as the end of the pipe), the wave will reflect back. However, this reflected wave will be shifted out of phase. As a result, the reflected wave will interact with the incident wave, and the two will interfere. This interference takes on a specific pattern in which there is destructive interference in the location of nodes, and constructive interference in the location of the antinodes. In such a situation, it doesn't appear that the wave is traveling at all, but rather it looks as if it's standing still, hence the name standing wave.
To solve this question, we need to use the expression for a pipe closed at one end and open at the other.
With this expression, we just need to plug in the values given to us in the question to solve for the length of the pipe.
Certified Tutor