How do we find the harmonic number ?

If you know the length of the medium ($L$) and the wavelength ($\lambda$) of the standing wave, you can rearrange the formula $L = n \frac{\lambda}{2}$ to solve for $n$:

$$n = \frac{2L}{\lambda}$$

For example, if $L = 1.0 \text{ m}$ and $\lambda = 0.5 \text{ m}$, then $n = \frac{2 \times 1.0 \text{ m}}{0.5 \text{ m}} = 4$.

For a standing wave with open ends on both sides (meaning antinodes at both ends), the harmonic number ($n$) is simply the number of half-wavelengths (or "loops" or "segments") that fit into the length of the medium.

• If you see one "loop" (one antinode in the middle), $n=1$ (fundamental frequency).
• If you see two "loops" (two antinodes), $n=2$ (first overtone).
• If you see three "loops" (three antinodes), $n=3$ (second overtone), and so on.

In the previous problem you sent a photo of, the wire had fixed ends (nodes at both ends), and we counted 5 loops, so $n=5$. If it were open on both sides and showed 5 loops, $n$ would also be 5.