1. Harmonics

2. First or Fundamental Harmonic on a String fixed at both ends

3. 2nd Harmonic

4. 3rd Harmonic

5. Equation
n = 1, 2, 3 …

6. First Harmonic of a Pipe open at both ends

7. 2nd Harmonic

8. 3rd Harmonic

9. Equation
n = 1, 2, 3 …

10. First Harmonic of a Pipe closed at one end

11. 2nd Harmonic? Open End of the pipe- not fixed so can’t be a node.

12. 3rd Harmonic

13. 5th Harmonic

14. Equation
n = 1, 3, 5 …

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