| Stationary wave energy transfer | Stationary waves do not transfer energy; they only store it, oscillating between kinetic and potential forms at nodes and antinodes. |
| Nodes in a stationary wave | Points of zero displacement where the medium is permanently at rest; energy is not transferred past these points. |
| Antinodes in a stationary wave | Points of maximum displacement where the medium oscillates with greatest amplitude; energy is stored here. |
| How are stationary waves formed? | By the superposition of two identical waves travelling in opposite directions, e.g. incident and reflected waves. |
| Phase difference between particles in a stationary wave | All particles between two consecutive nodes oscillate in phase; particles on opposite sides of a node oscillate in anti-phase. |
| Wavelength of a stationary wave | Twice the distance between two consecutive nodes (or antinodes): \lambda = 2 \times \text{node spacing}. |
| Frequency of a stationary wave | Same as the frequency of the two travelling waves that produce it. |
| First harmonic (fundamental) of a string fixed at both ends | One antinode at centre, nodes at both ends; length L = \frac{\lambda}{2} so \lambda = 2L. |
| Second harmonic of a string fixed at both ends | Two antinodes and three nodes; length L = \lambda so \lambda = L. |
| Third harmonic of a string fixed at both ends | Three antinodes and four nodes; length L = \frac{3\lambda}{2} so \lambda = \frac{2L}{3}. |
| How to calculate harmonic frequencies on a string | f_n = n \times f_1 where n = 1, 2, 3,\ldots and f_1 = \frac{v}{2L}. |
| Speed of wave on a string formula | v = \sqrt{\frac{T}{\mu}} where T is tension and \mu is mass per unit length. |
| Effect of increasing tension on stationary wave frequency | Frequency increases because wave speed increases (v = \sqrt{T/\mu}) while wavelength remains fixed by boundaries. |
| Effect of increasing string density on stationary wave frequency | Frequency decreases because wave speed decreases (v = \sqrt{T/\mu}) for fixed tension. |
| Open air column stationary wave (both ends open) | Antinodes at both open ends, node(s) in between; fundamental: \lambda = 2L. |
| Closed air column stationary wave (one end closed) | Node at closed end, antinode at open end; fundamental: \lambda = 4L. |
| Overtones of a closed air column | Only odd harmonics: f_n = n f_1 where n = 1, 3, 5,\ldots; fundamental \lambda = 4L. |
| How to find node positions in a stationary wave | Nodes occur where the path difference between incident and reflected waves is an odd multiple of \frac{\lambda}{2}. |
| Energy in a stationary wave | Total energy is constant but oscillates periodically between kinetic energy (at antinodes) and potential energy (near nodes). |