Closed-Open Tube

Displacement waves in tube closed at one end:

Figure 3: Standing waves for displacement in an closed-open tube

The wavelength of the first harmonic is $\lambda_1 = 4L$.

Adding an antinode/node creates the next standing wave pattern with wavelength $${\lambda_3 = \frac{4}{3}L}$$

Since $\lambda_3$ is $1/3^{\mbox{rd}}$ the length of $\lambda_1$, the frequency is 3 times the fundamental and it is the “third” harmonic.

Notice the second harmonic is missing!