Final answer:
The boundary conditions for the modality principle require a node at each end. The first mode shows half of a wavelength and the second mode is found by adding a half wavelength.
Step-by-step explanation:
The boundary conditions for the modality principle are that there must be a node at each end. The first mode, also known as the fundamental mode or the first harmonic, shows half of a wavelength and the wavelength is equal to twice the length between the nodes.
For example, if we have a string with a node at each end, the first mode will be half of a wave. The second mode can be found by adding a half wavelength, and this is the shortest length that will result in a node at the boundaries.
In a medium that is free to oscillate on each end, the boundary conditions would have antinodes at each end.