IB Physics Standing Waves: Concept & Exam Guide

A standing (stationary) wave forms when two identical waves travelling in opposite directions superpose — usually an incident wave and its reflection. Unlike a travelling wave, it doesn't transfer energy along its length; it has fixed nodes (zero displacement) and antinodes (maximum displacement). It's examined in Topic 4 (SL & HL) via diagrams, harmonic calculations and short-answer or data-based questions.

A travelling wave carries energy from one point to another and every particle along it has the same amplitude, just a phase delay. A standing wave stores energy locally — particles between adjacent nodes oscillate in phase but with different amplitudes, and no net energy moves past a node. That's the one-sentence answer examiners want on a 'compare' question.

A node is a point on a standing wave with zero displacement at all times — the wave's amplitude is always zero there. An antinode is a point of maximum displacement, oscillating with the largest amplitude in the pattern. Adjacent nodes are always separated by half a wavelength, and an antinode sits exactly midway between them.

For a string fixed at both ends, the nth harmonic frequency is $f_n=\frac{nv}{2L}$, where $v$ is wave speed, $L$ is string length, and $n=1,2,3\dots$. The fundamental ($n=1$) has one antinode and two nodes; each higher harmonic adds one more node and antinode.

An open-open pipe has an antinode at each open end and supports all harmonics: $f_n=\frac{nv}{2L}$. A closed-open pipe has a node at the closed end and an antinode at the open end, supporting only odd harmonics: $f_n=\frac{nv}{4L}$ for $n=1,3,5\dots$. Mixing these two formulas up is the single most common exam error on this topic.

Because the closed end must always be a node and the open end must always be an antinode, only wave patterns that fit a node at one end and antinode at the other are physically possible. That geometric constraint only allows odd multiples of the quarter-wavelength pattern — the even harmonics simply don't satisfy both boundary conditions simultaneously.

The three recurring errors I see every year marking mocks: mixing up the open-pipe and closed-pipe harmonic formulas, forgetting that wavelength (not distance between nodes) equals twice the node-to-node spacing when reading off diagrams, and describing standing waves as 'transferring no energy at all' instead of 'no net energy transfer past a node'.

Paper 1 (multiple choice) usually tests quick harmonic-number or wavelength identification from a diagram. Paper 2 typically gives a longer structured question: derive a frequency, explain formation using superposition, or link resonance to a real-world scenario like a wine glass or bridge. HL papers sometimes extend into diffraction gratings or the Doppler effect within the same question.

You need $f_n=nv/2L$ for strings and open-open pipes, $f_n=nv/4L$ (odd n only) for closed-open pipes, and $v=\sqrt{T/\mu }$ for wave speed on a string. The IB Physics data booklet gives most wave equations, but not always the harmonic-number relationships — you're expected to derive those from the boundary conditions on the spot.

The core concept — nodes, antinodes, harmonic formulas for strings and pipes — is shared by SL and HL students. HL students go further, connecting standing waves to diffraction gratings, resonance in more complex systems, and sometimes multi-step problems combining wave phenomena with the Doppler effect in the same question.

Resonance happens when a system is driven at one of its natural (harmonic) frequencies, causing a standing wave pattern to build up with large, stable amplitude. A guitar string resonates at its fundamental and harmonics; an organ pipe resonates at the frequencies allowed by its boundary conditions. Standing waves are essentially what resonance looks like once it's established.

Standing waves is one sub-topic within the broader Waves topic, so it won't sink an overall grade on its own — but it recurs across Paper 1 and Paper 2, and often reappears combined with resonance or the Doppler effect in the same question. Getting the boundary-condition logic solid early pays off across several exam questions, not just one.