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Throughout this module we have been careful to distinguish the two fundamentally different types of wave: the progressive (or travelling) wave, which carries energy through space, and the stationary (or standing) wave, which stores energy locally in the form of oscillations. This final lesson draws together all the differences and similarities, provides a full comparison, and explores some applications that illustrate the concepts in real contexts. By the end, you should be able to explain in a single paragraph exactly how the two kinds of wave differ — a staple of OCR exam questions.
| Property | Progressive wave | Stationary wave |
|---|---|---|
| Energy transfer | Yes — energy is carried along the wave | No — energy is stored in the oscillation and does not propagate |
| Waveform movement | The pattern of crests and troughs moves through space | The pattern is fixed in space; only the amplitudes oscillate in time |
| Amplitude | All particles oscillate with the same amplitude (A) | Amplitude varies from zero (nodes) to maximum (antinodes) |
| Phase | Neighbouring particles are in continuously varying phase — phase increases smoothly along the wave | All particles between two adjacent nodes are exactly in phase; particles on opposite sides of a node are in antiphase (π rad different) |
| Formation | A single source emits the wave | Requires superposition of two progressive waves of equal amplitude and frequency travelling in opposite directions (usually a wave and its reflection) |
| Wavelength measurement | Distance between two adjacent points in phase | Twice the distance between two adjacent nodes (= twice the distance between two adjacent antinodes) |
| Examples | Sound from a speaker, EM radiation, surface water waves, seismic waves | Vibrating guitar string, organ pipe, resonating wine glass, microwave oven |
Commit this table to memory. Any OCR question asking to "compare stationary and progressive waves" should draw on at least three or four of these rows in the answer.
The most fundamental distinction is about energy.
In a progressive wave, energy continually flows through each cross-section of the medium. A loudspeaker broadcasts sound energy into the air; the waves carry that energy outward to the listener; the energy is delivered and absorbed. Mathematically, the intensity I (power per unit area) is a non-zero quantity:
I ∝ A² for a progressive wave
In a stationary wave, the energy stays in the region where the wave is set up. Each element of the medium oscillates about its equilibrium position — so kinetic and potential energy slosh back and forth within each half-wavelength cell — but no net power flows through any fixed plane. A plucked guitar string vibrates audibly for seconds, slowly losing energy to the air and to friction, but the energy does not travel along the string; it is local to the part of the string that is vibrating.
This is why musical instruments can be played repeatedly without needing to replenish their strings — the energy you put in with each pluck or bow stroke stays in the string until it is gradually radiated (as sound) or damped (by friction in the instrument body). The audible sound itself is a progressive wave, radiated by the string into the surrounding air.
Another diagnostic distinction is amplitude as a function of position.
In a progressive wave, every particle has the same maximum displacement from equilibrium. If you mark two points on a wave-carrying rope, both will eventually reach exactly the amplitude A.
In a stationary wave, the amplitude varies from point to point. At an antinode, the oscillation amplitude is maximum (2A, where A is the amplitude of the constituent travelling waves). At a node, the amplitude is zero — the particle at that point never moves. Between nodes and antinodes, intermediate amplitudes occur.
You can actually see this distinction by freezing-frame imagination: a progressive wave on a rope, stopped in time, looks like a sinusoid of uniform amplitude running along the rope; a stationary wave, stopped, looks like a sinusoid that is modulated — smaller in some places, larger in others — with zeros at regular intervals.
The phase differences between particles also distinguish the two types of wave.
In a progressive wave, particles separated by a distance d have phase difference φ = 2πd/λ. Neighbouring particles are slightly out of phase with each other (with a small, smooth phase shift); particles λ/2 apart are in antiphase; particles λ apart are back in phase; and so on.
In a stationary wave, the phase relationships are discrete:
This is a striking feature of stationary waves and can be demonstrated visually with a slow-motion video of a vibrating string.
Since there are no "progressing" wavefronts in a stationary wave, the idea of "wavelength" needs careful definition. The standard convention is that the wavelength λ of a stationary wave is the wavelength of the underlying travelling waves that superposed to create it. In practice this means:
λ (stationary wave) = 2 × (node-to-node distance) = 2 × (antinode-to-antinode distance)
If you measure 25 cm between two adjacent nodes on a rope in a lab demonstration, the wavelength is 50 cm.
Stationary waves are almost always formed when a progressive wave is reflected back on itself — the incoming wave and the reflected wave superpose. For this to give a clean stationary pattern, the reflection must happen at a well-defined end with well-defined boundary conditions:
Musical instruments exploit these boundary conditions to control which frequencies are supported. A guitar string (both ends fixed) supports nodes at both ends; a flute (both ends open) supports antinodes at both ends; a clarinet (closed at the mouthpiece, open at the bell) supports a node at the mouthpiece and an antinode at the bell — which is why clarinets produce only odd harmonics.
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