A stationary (standing) wave forms when two progressive waves with the same frequency and similar amplitude travel in opposite directions and superpose. This usually happens when a wave reflects back on itself, for example at the fixed end of a string.The pattern does not move along. At some points the two waves always cancel. These are nodes, points of zero amplitude. Halfway between nodes the waves reinforce to give the largest oscillation. These are antinodes, points of maximum amplitude.
The distance between adjacent nodes (or adjacent antinodes) is λ/2. The distance from a node to the next antinode is λ/4.
All points between two adjacent nodes oscillate in phase. Points on opposite sides of a node are in antiphase.
The amplitude varies with position, from zero at a node to a maximum at an antinode.
No energy is transferred along a stationary wave. Energy is stored in the oscillation.Compare this with a progressive wave, where every point has the same amplitude, the phase changes steadily along the wave, and energy is transferred.Worked example: adjacent nodes on a stationary wave are 0.15 m apart. The wavelength is 2 × 0.15 = 0.30 m. If the frequency is 1000 Hz, the speed of the progressive waves that formed it is v = fλ = 1000 × 0.30 = 300 m s-1.
The distance between adjacent nodes (or adjacent antinodes) is λ/2. The distance from a node to the next antinode is λ/4.
All points between two adjacent nodes oscillate in phase. Points on opposite sides of a node are in antiphase.
The amplitude varies with position, from zero at a node to a maximum at an antinode.
No energy is transferred along a stationary wave. Energy is stored in the oscillation.Compare this with a progressive wave, where every point has the same amplitude, the phase changes steadily along the wave, and energy is transferred.Worked example: adjacent nodes on a stationary wave are 0.15 m apart. The wavelength is 2 × 0.15 = 0.30 m. If the frequency is 1000 Hz, the speed of the progressive waves that formed it is v = fλ = 1000 × 0.30 = 300 m s-1.