Final answer:
In a stationary wave on a fixed string, the harmonic number n is not directly equal to the number of nodes or antinodes. The nodes are points of zero amplitude and there are n-1 nodes and n antinodes in the nth harmonic. The energy of the standing waves increases with the number of nodes.
Step-by-step explanation:
For a stationary wave on a fixed string, the harmonic number n does not equal the number of nodes or antinodes directly. Instead, the relationship involves the concept of standing wave patterns that can be established within a constrained medium, such as a string that is fixed at both ends. With each harmonic or standing wave mode, an integer number of half-wavelengths fits into the length of the string.
In the n'th harmonic, there are n - 1 nodes and n antinodes within the string. The nodes represent points of zero amplitude, where the medium does not move. Antinodes, by contrast, are points of maximum amplitude in a standing wave pattern. The wavelength is inversely related to the number of antinodes and can be determined by the distance between the string's fixed points.
The relationship between the number of nodes and harmonics is such that the energies of the standing waves increase with the number of half-wavelengths, thereby generally increasing as the number of nodes increases. Ultimately, for any given harmonic on a string, the number of nodes is always one less than the harmonic number, so the harmonic number n is not equal to the number of nodes nor antinodes directly.