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What is a standing (stationary) wave?
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All Flashcards in Topic 3.4
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3.4.112 cards
What is a standing (stationary) wave?
The fixed pattern made when **two identical waves travel in opposite directions** and superpose — it does not move along.
What is superposition?
When two waves overlap, you **add their displacements** at every point to get the total wave.
Define a node.
A point on a standing wave that **never moves** (zero displacement) — the two waves always cancel there.
Define an antinode.
A point on a standing wave that swings with the **largest amplitude**, halfway between two nodes.
How far apart are neighbouring nodes?
**Half a wavelength (λ/2).** So λ = 2 × the node-to-node spacing. (Not in the data booklet — remember it.)
Does a standing wave transfer energy along its length?
**No** — there is no net energy transfer along a standing wave; the energy stays stored in place.
Phase of points between two nodes?
They move **in phase** (all together). Points on opposite sides of a node move in **antiphase** (exactly opposite).
Standing wave vs travelling wave — phase?
Standing: points are only ever **in phase or antiphase**. Travelling: the phase shifts **smoothly** from point to point.
How is a standing wave usually produced?
A wave **reflects off a fixed end** and meets itself coming back — two identical opposite waves that superpose.
Why does chocolate melt in spots in a microwave?
Microwaves reflect off the walls and form a **standing wave**; the field is strongest at the **antinodes**, so it melts there and stays solid at the nodes.
Melted spots are 6.0 cm apart — what is the wavelength?
Spots are one antinode apart = λ/2, so λ = 2 × 0.060 = 0.12 m.
Most common standing-wave mistake?
Thinking it **carries energy along** the string, or halving (instead of doubling) the node spacing to get the wavelength.
3.4.212 cards
What is a node?
A point on a standing wave that **never moves** (zero amplitude).
What is an antinode?
A point on a standing wave that swings with the **largest** amplitude.
What is the fundamental (1st harmonic)?
The **lowest** frequency at which a string or air column resonates — the standing-wave pattern with the fewest loops.
What is resonance?
When a system is driven at one of its **natural frequencies** and vibrates with a large amplitude — that is what makes a harmonic loud.
Wavelength condition for a string fixed at both ends (or a pipe open at both ends)?
**λ = 2L/n** for n = 1, 2, 3, … — n half-wavelengths fit into the length L.
Wavelength condition for a pipe closed at one end?
**λ = 4L/n** with **n = 1, 3, 5, …** (odd harmonics only — node at the closed end, antinode at the open end).
Are λ = 2L/n and λ = 4L/n in the data booklet?
**No** — you must memorise them. Only the wave equation v = fλ is given.
Why does a pipe closed at one end have only odd harmonics?
Its ends are different (node at the closed end, antinode at the open end), so only odd numbers of quarter-wavelengths fit: λ = 4L/n, n = 1, 3, 5, …
How far apart are two neighbouring nodes (or antinodes)?
**Half a wavelength.** So λ = 2 × the node-to-node spacing.
How do you turn a wavelength into a frequency?
Use the given wave equation **v = fλ**, rearranged to **f = v ÷ λ** (v is the wave speed — the speed of sound for a pipe).
A 0.65 m string fixed both ends, wave speed 260 m s⁻¹ — fundamental frequency?
λ = 2L = 1.3 m; f = v/λ = 260/1.3 = 200 Hz.
How can melted spots in a microwave give the microwave frequency?
The spots (antinodes) are half a wavelength apart; double the spacing for λ, then f = c/λ.
Topic 3.4 study notes
Full notes & explanations for Standing waves and resonance
Physics exam skills
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