Explanation:

For \(p\) number of loops in a stretched string, the length is given by
\(l = \frac{{p\lambda }}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
As, number of harmonics \(=\) number of loops \(=\) number of anti nodes \( = p\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
Also, number of nodes \(=\) number of anti nodes \(+1\)
Here, number of nodes \( = m\)
Number of anti nodes \( = m - 1\)
from eq.(2)
\(p = m - 1\)
Putting this value of \(p\) in eq .(1), we get
\(l=\dfrac{(m-1) \lambda}{2}\)