Standing Waves and Harmonics Standing Wave If the

Standing Waves and Harmonics

Standing Wave If the pulses of a periodic wave are reflected so that the reflections interfere with the incident wave in the proper manner a standing wave will result.

Equations Incident wave Reflected wave Standing Wave Trig Identity

Standing Wave

Standing Wave Animation http: //www. kettering. edu/~drussell/Demos. html

Nodes and Antinodes Antinode – area of large displacement Node – area of no or little displacement

Examples

First or Fundamental Harmonic on a String fixed at both ends http: //www. physicsclassroom. com/Class/sound/U 11 L 4 c. html

2 nd Harmonic http: //www. physicsclassroom. com/Class/sound/U 11 L 4 c. html

3 rd Harmonic http: //www. physicsclassroom. com/Class/sound/U 11 L 4 c. html

Equation For Constant L n=1 n=2 n=3 n = 1, 2, 3 …

Constant Frequency n = 1, 2, 3 … Note that if the frequency and velocity are constant and the length is varied each harmonic will occur at a length ½ wavelength greater than the previous harmonic.

First Harmonic of a Pipe open at both ends http: //www. physicsclassroom. com/Class/sound/U 11 L 5 c. html

2 nd Harmonic http: //www. physicsclassroom. com/Class/sound/U 11 L 5 c. html

3 rd Harmonic http: //www. physicsclassroom. com/Class/sound/U 11 L 5 c. html

Equation For Constant L n = 1, 2, 3 … Be aware that in reality a vibrating column of air extends slightly beyond the pipe, so L is actually greater than the length of the pipe.

First Harmonic of a Pipe closed at one end http: //www. physicsclassroom. com/Class/sound/U 11 L 5 d. html

2 nd Harmonic? Open End of the pipenot fixed so can’t be a node. http: //www. physicsclassroom. com/Class/sound/U 11 L 5 d. html

3 rd Harmonic http: //www. physicsclassroom. com/Class/sound/U 11 L 5 d. html

5 th Harmonic http: //www. physicsclassroom. com/Class/sound/U 11 L 5 d. html

Equation For Constant L n=1 n=3 n=5 n = 1, 3, 5 …

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

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