Nodes & Antinodes
Highlighted N and A on a vibrating string.
Key Notes
NODES: points of ZERO displacement in a standing wave — always at rest.
ANTINODES: points of MAXIMUM displacement — oscillate with amplitude 2A.
Nodes and antinodes ALTERNATE along the wave; spacing between consecutive nodes (or antinodes) = λ/2.
Distance from node to NEAREST antinode = λ/4.
For a string FIXED at both ends: ends are nodes. Allowed λ = 2L/n (n = 1, 2, 3, …).
For a tube CLOSED at one end (open at other): closed end is node, open is antinode. Allowed λ = 4L/(2n−1).
For a tube OPEN at both ends: both ends are antinodes. Allowed λ = 2L/n.
Number of nodes & antinodes determines the HARMONIC number.
Formulas
Position of nodes (kL convention)
Spaced every λ/2.
Position of antinodes
Halfway between nodes.
Allowed wavelengths (string)
Fundamental + harmonics.
Allowed wavelengths (open pipe)
Same as string fixed both ends.
Closed pipe
Only odd harmonics: 1st, 3rd, 5th, …
Important Points
Distance node-to-node (or antinode-to-antinode) = λ/2.
Distance node-to-antinode = λ/4.
Fundamental mode (n=1): LARGEST λ, LOWEST f. Higher harmonics have shorter λ, higher f.
Boundary conditions DETERMINE which λ are allowed.
Sound antinodes have max DISPLACEMENT but min PRESSURE; nodes have max PRESSURE.
In a tube, blowing harder doesn't change f much — just amplifies harmonics already present.
Nodes & Antinodes notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.