- \(\lambda = {{al} \div n}\quad\) (\(\lambda\) for \(n^{th}\) harmonic)\\
- \(f = {nv \div al}\quad\) (\(f\) for \(n_{th}\) harmonic at length
- \(l\) and speed \(v\)) \\
- where \(a=2\) for antinodes at both ends, \(a=4\) for antinodes at one end
+ 1st harmonic = fundamental
+
+ \textbf{for nodes at both ends:} \\
+ \(\hspace{2em} \lambda = {{2l} \div n}\)
+ \(\hspace{2em} f = {nv \div 2l} \)
+
+ \textbf{for node at one end ($n$ is odd):} \\
+ \(\hspace{2em} \lambda = {{4l} \div n}\)
+ \(\hspace{2em} f = {nv \div 4l} \) \\
+ alternatively, $\lambda = {4l \over {2n-1}}$ where $n\in \mathbb{Z}$ and $n+1$ is the next possible harmonic
+
+
+ % \(a=2\) for nodes at both ends, \\ \(a=4\) for node at one end