# How to visualize the propagation of a wave?

Waves can be visualized as a waveform, with crests, troughs, wavelength and amplitude. Water waves (wind waves) fits excellent in this model. However, there is many kind of waves in nature. Is it correct to say that all waves propagate in this way?

1. Pressure waves (sound) is more like a compression and rarefaction, which propagate in a straight line. Is the waveform the wrong approach to those waves? Do they really swing up and down? Or is it the right approach, because the amplitude is too low to be noticed normally?

2. Is it correct to assign the waveform to classical electromagnetic waves? Do they really swing up and down as the waveform say? If we for example shine a ray of light in one direction, will the light swing up and down, and the meter over sea level will differ very slightly?

3. And what about the quantum mechanical photon and other elementary particles? Is it also correct to model them as a waveform? Does they really swing up and down? This sounds unlikely because of the uncertainty principle of quantum mechanics. However, I see everywhere that the path to a particle is pictured as a waveform. Is this approach completely misleading? If so, what is the correct visualization for the propagation of elementary particles? (I guess I am asking how to visualize the wave function).

• Waves need not necessarily be "waves": any function solving the wave equation, namely any function that can be expanded in series of plane waves $e^{i(kx-\omega t)}$ is a wave. – gented Jul 12 '17 at 17:47

To answer some of your questions. Indeed sound waves can be thought as compression. They are actually longitudinal waves. The sound propagates by the difference in air pressure and by the appearance of a gradient (sudden) change in the density of air molecules. So you need something in the medium to move in order to have the propagation of sound: That's why you can't hear anything in space.

The electromagnetic waves have transversal nature. They are composed of two fields which are oscillating and generating each other as they move. You can see them as bumps (crests, troughs). If you generate an E.M wave and try to record it, you can see it as a sine wave or other forms (most of them oscillating). Photons are waves or particles depending on what kind of experiment are you studying. For example, in interference, the photon can be seen as a wave. But in photoelectric effect, the photons are considered as articles. The idea of wave-particle duality is a key concept in Q.M.. In a way, it is correct to consider all the particles you know as some"clouds", where that cloud represents the probability amplitude that you will find the particle.

Hope this helps!

The up and down variations of classical systems are variations in amplitude of sinusoidal descriptions of waves. Wave equations fit wave phenomena classically with sine and cosine functions of space and time.

Take the electromagnetic wave, (light is part of the spectrum) the classical solution of maxwell's equations where the amplitude represents electric and magnetic fields, which are dirrectly connected with the energy transferred by the wave.

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together

The same is true for acoustic waves, the rarification and compression propagates the energy sinusoidally in space and time.

In general classical waves have a form of "energy waving" , energy is transferred with the wave.

And what about the quantum mechanical photon and other elementary particles? Is it also correct to model them as a waveform?

It is a wave form which is described by the quantum mechanical wavefunctions, but what is "waving" is the probability distribution for finding a particle at (x,y,z,t). It is not an energy distribution.

Electron buildup over time

In this double slit experiment one electron at a time:

each individual particle seems random, it is the the accumulated probability distribution that shows wave interference.

The same is true for individual photons. Nothing swings up and down except the probability calculated by the wavefunction's Complex conjugate squared.

• can I ask if there is a trick to uploading an animated gif. I tried and it did not work: basically imgur just shows the first image. Thanx. – ZeroTheHero Jul 17 '17 at 22:44
• @ZeroTheHero I tried to repeat this feat a few days ago and got the same result as you, and did not try to re discover what I had done. later: Ok, went through all possibilities once more, and what works is to save the image on desktop ( windows 10) and load it from there . – anna v Jul 18 '17 at 3:54
• Thanks... I just reloaded my own image and it seemed to work. I thought I had done it from the desktop before but maybe not... anyways it's fixed now. Thanks again. – ZeroTheHero Jul 19 '17 at 15:30