8.1 Stationary waves

When waves overlap, the resultant displacement at each point is the algebraic sum of the individual displacements: y=y₁+y₂.

Keep signs and phases, then add the contributions at the same position and time. The waves continue afterwards rather than permanently merging.

Two equal pulses with the same sign reinforce to double displacement; opposite pulses can cancel temporarily.

Superposition does not mean one wave destroys the other or that energy disappears when displacement is zero.

Reflected and incident microwaves can form a stationary pattern. A probe finds alternating nodes of minimum signal and antinodes of maximum signal.

The distance between adjacent nodes or adjacent antinodes is λ/2, so scan spacing must be doubled to obtain wavelength.

If adjacent signal minima are 1.5 cm apart, the microwave wavelength is 3.0 cm.

A node is not half a wavelength apart from the next antinode; node-to-antinode spacing is λ/4.

A stationary wave results when two coherent waves of the same frequency, speed and amplitude travel in opposite directions and superpose.

The pattern has fixed nodes and antinodes, so there is no net energy transfer along the medium even though particles oscillate between them.

A string driven at one end and reflected at the other can settle into a pattern with several loops separated by nodes.

A stationary wave is not a wave travelling slowly; its nodes remain fixed while local oscillations continue.

In a stationary wave, adjacent nodes or adjacent antinodes are separated by λ/2; a node to the nearest antinode is λ/4.

Measure over several intervals when possible, divide by the number of half-wavelength gaps, then multiply by two.

Four adjacent node gaps spanning 12 cm give λ=2×(12/4)=6.0 cm.

Counting positions rather than gaps gives an off-by-one error; the end-to-end distance must be divided by the number of intervals.