Harmonics.

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Presentation transcript:

Harmonics

First or Fundamental Harmonic on a String fixed at both ends http://www.physicsclassroom.com/Class/sound/U11L4c.html

2nd Harmonic http://www.physicsclassroom.com/Class/sound/U11L4c.html

3rd Harmonic http://www.physicsclassroom.com/Class/sound/U11L4c.html

Equation n = 1, 2, 3 …

First Harmonic of a Pipe open at both ends http://www.physicsclassroom.com/Class/sound/U11L5c.html

2nd Harmonic http://www.physicsclassroom.com/Class/sound/U11L5c.html

3rd Harmonic http://www.physicsclassroom.com/Class/sound/U11L5c.html

Equation n = 1, 2, 3 …

First Harmonic of a Pipe closed at one end http://www.physicsclassroom.com/Class/sound/U11L5d.html

2nd Harmonic? Open End of the pipe- not fixed so can’t be a node. http://www.physicsclassroom.com/Class/sound/U11L5d.html

3rd Harmonic http://www.physicsclassroom.com/Class/sound/U11L5d.html

5th Harmonic http://www.physicsclassroom.com/Class/sound/U11L5d.html

Equation n = 1, 3, 5 …

Summary Harmonics for strings and open-ended pipes n = 1, 2, 3 … Harmonics for pipes with one closed end n = 1, 3, 5 …