Main Difference – Stationary vs. Progressive Waves

The oscillation of particles in a wave contains some energy. Depending on what happens to the energy in a wave, we can classify waves into stationary waves (standing waves) and progressive waves (travelling waves). The main difference between stationary and progressive waves is that progressive waves transfer energy from one place to another whereas stationary waves do not transfer energy from one place to another.

What are Progressive Waves (Travelling Waves)

Progressive waves transfer energy from one place to another, without transferring the matter. In progressive mechanical waves, one oscillating molecule transfers some of its energy to the next molecule and then, that molecule starts oscillating as well. This molecule now transfers energy to the next molecule,… and so on the energy is transferred along the wave. In the case of electromagnetic waves, the changes in the electric and magnetic fields carry the energy of the wave.

The light coming from the Sun is an example of a progressive wave. The oscillations in the electric and magnetic fields bring energy all the way from the Sun to the Earth. In a progressive wave, two neighbouring points are never in phase with each other. Suppose a point A along the wave is at a specific phase. If A has a neighbouring point B and if the wave is being propagated in the direction from A to B, then point B acquires A’s phase a moment after A does. While this is happening, A is also changing its phase, so A and B will never be in phase with each other. Consequently, if A acquires its “amplitude” (i.e. maximum displacement from equilibrium) at a given time, B acquires its amplitude a moment later, but by this time A is no longer at the amplitude value.

What are Stationary Waves (Standing Waves)

Stationary waves do not transfer energy from one place to another. Instead, they “store” their energy in one place. Stationary waves are formed when two progressive waves with the same frequency and similar amplitudes, travelling in opposite directions, interfere with each other. If you look at a standing wave, it would seem as though it is made of “loops”. The “middles” of these loops are called antinodes and the “edges” of these loops are called nodes, as shown below:

Stationary waves: nodes and antinodes

Nodes form in places where the two progressive waves interfere in antiphase. Antinodes form in places where the two progressive waves interfere in phase. Note that this type of stable pattern forms only at specific frequencies, called harmonic frequencies. At other frequencies, the phase relationship between the two progressive waves at any point is not constant, and so you would not be able to see a clear, stable pattern.  This following video offers a great demonstration, showing how a standing wave is formed on a vibrating rope.

In stationary waves, every point “within a loop” (i.e. between two successive nodes) is in phase. This means that all oscillations reach amplitude simultaneously. However, no two neighbouring points along a stationary wave have the same amplitude. A point at an antinode has the maximum amplitude while a point at a node has an amplitude of 0. Points in two “neighbouring loops” in a stationary wave are in antiphase with each other. The distance between two successive nodes (or two successive antinodes) in a stationary wave is equal to half of the wavelength.

Waves produced by guitar strings are stationary waves. When you pluck a string, you create a progressive wave that travels along the string and gets reflected at the end of the string. The original wave interferes with the reflected wave and forms a stationary wave. Flutes and other wind instruments also produce stationary waves. These stationary waves are produced by the oscillation of air molecules in the air columns in those instruments.

Difference Between Stationary and Progressive Waves

Energy Transfer

Progressive waves transfer energy from one place to another, without transferring the matter.

Stationary waves do not transfer energy from one place to another.

Phase Relationship between Neighbouring Points

In progressive waves, two neighbouring points are not in the same phase.

In stationary waves, all points between two successive nodes are in the same phase.

Amplitude

In progressive waves, each point achieves the same amplitude.

In stationary waves, different points achieve different amplitudes.

Image Courtesy

“Standing Wave with node and antinode shown…” by Vegar Ottesen (Own work) [CC BY-SA 3.0], via Wikimedia Commons

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