At what electromagnetic frequency does the wavelength = the wave height?

Question

At what frequency does the wavelength equal the height of the wave amplitude?

The wave height / amplitude the physical space the wave height occupy in space, similar to the wavelength. My assumption is that the wave height of the basic electromagnetic wave is fixed.

It is my understanding that, fixed amplitude in E.M. graph can be:

• Pictures of the electromagnetic spectrum, shows that the amplitude is the same regardless of frequency. what is the amplitude used in these Pictures?
• The maximum photons emitted by single electron per second.
• The minimum photons needed to make light wave ???.

Now, let's ignore the typical E.M. wave graph and only take the wavelength from it. As we know, the E.M. waves propagate from left to right or up to down as mentioned by annav down below and here. The next step is to calculate the length of the up to down motion in physical space most likely it will be in Planck and compare it to the wavelength. At what frequency does the wavelength equal the length of the left to right \ up to down motion?

Follow up question: does the length of the up to down motion change with the frequency??

Answer 1

The electromagnetic wave is not a wave on a medium, as water waves which are coherent variations in position of water molecules.

Electromagnetic waves are built up by photons in coherence , each photon having an energy h*nu where nu is the frequency of the wave that emerges from a large number of photons . ( to get an idea of how many look at my answer here) .

The photons, as quantum mechanical entities, are described by a wavefunction which is a solution of a quantized maxwell's equation. This wave function has information on the electric an magnetic fields that will be built up in the emergent classical wave.

The emergent classical electromagnetic wave

The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized EMR wave propagating from left to right (X axis). The electric field is in a vertical plane (Z axis) and the magnetic field in a horizontal plane (Y axis). The electric and magnetic fields in EMR waves are always in phase and at 90 degrees to each other.

This is an instance in time

In the same link there is an animation that shows the propagation in time.

The equations for the electric and magnetic field are:

and to be consistent solutions of maxwell's equations:

The magnitude of the E and B fields, the E_m and B_m depends on the energy carried by the specific electromagnetic wave:

As you can see, the wavelength develops in space, but the height of the wave, as everybody has been trying to explain the comments, is not in units of length, but in units of the electric E field and the corresponding units of c*B field. Thus your question has no answer because it compares apples to oranges.

The connection is not simple even in water waves, whose height is in the units of space.

Answer 2

At what frequency does the wavelength = the height of the wave amplitude ?

At 7.7646 x 10²⁰ Hz. The associated wavelength and amplitude is 3.861 x 10⁻¹³ m. The electron Compton wavelength is 2.426 × 10⁻¹² m, which is 2π times this amplitude.

The wave height = the physical space the waveheight occupy in space, similar to the wavelength. My assumption is that the wave height of the basic electromagnetic wave is fixed.

Correct. Take a look at some pictures of the electromagnetic spectrum, note that the amplitude is the same regardless of frequency, and note that the dimensionality of action h can be expressed as momentum x distance. Also note that the reduced Planck's constant ħ is h divided by 2π.

It's important to note that an electromagnetic wave is an electromagnetic wave. Some people will tell you it's an electric wave and a magnetic wave which generate one another, and therefore no medium is required. That's not true. Check out the Wikipedia electromagnetic wave article and note this:

"Also, E and B far-fields in free space, which as wave solutions depend primarily on these two Maxwell equations, are in-phase with each other. This is guaranteed since the generic wave solution is first order in both space and time, and the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field".

What people call the electric wave is actually the spatial derivative of the electromagnetic wave, while the magnetic wave is actually the time derivative. They are merely two aspects of the same wave, not two different waves. And as Maxwell said, "light consists of transverse undulations in the same medium that is the cause of electric and magnetic phenomena". When an ocean wave travels through the sea, the sea waves. When a seismic wave travels through the ground, the ground waves. When a gravitational wave travels through space, space waves. See LIGO:

"Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity. Einstein's mathematics showed that massive accelerating objects (such as neutron stars or black holes orbiting each other) would disrupt space-time in such a way that 'waves' of distorted space would radiate from the source (like the movement of waves away from a stone thrown into a pond)".

The same is true for an electromagnetic wave. When an electromagnetic wave travels through space, space waves.