A string’s nth mode has n+1 nodes and n antinodes

Evidence

It can be seen in Figure 4.6 that the first mode has two displacement nodes (at the ends of the string) and one displacement antinode (in the center). The sixth mode has seven displacement nodes and six displacement antinodes. In general, a particular mode (n) of a string fixed at both ends has (n + 1) displacement nodes and (n) displacement antinodes. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1081

Categorization

• DEFINE: Formal relationship between mode number and node/antinode count on a fixed string.
• XREF: connects to: Plucking a string at a node suppresses every Nth harmonic; Pinning a node makes higher modes act as fundamentals of shorter strings — Eric J. Heller, Why You Hear What You Hear- An…, 874; Plucking position on a string suppresses modes with nodes there — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1083 (+3 more)

Broader Connections

• Plucking a string at a node suppresses every Nth harmonic #expands (0.90)
• Plucking position on a string suppresses modes with nodes there #expands (0.88) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1083
• Plucking position on a string determines which harmonic modes are suppressed #expands (0.88) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1107
• Pinning a node makes higher modes act as fundamentals of shorter strings #expands (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 874
• Double-kink string modes produce the octave via a center node #exemplifies (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 1753
• Nodes are stationary points where a vibrating mode has no motion #expands (0.82) — Eric J. Heller, Why You Hear What You Hear- An…, 794