.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/communications/propagation/plot_01_hertz_wavelength.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_communications_propagation_plot_01_hertz_wavelength.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_communications_propagation_plot_01_hertz_wavelength.py:


Hertz's electromagnetic waves and their wavelength
==================================================

Maxwell's equations (1865) predicted electromagnetic waves travelling at the
speed of light. Heinrich Hertz confirmed them in 1887-1888: a spark gap drove
waves at a few hundred megahertz, a metal sheet reflected them into a
standing wave, and the spacing of the nodes, half a wavelength, multiplied by
the frequency gave the speed. :func:`~engineeringkit.communications.wavelength`
computes :math:`\lambda = c/f`; the example reconstructs Hertz's standing-wave
measurement and maps the radio spectrum.

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.communications import SPEED_OF_LIGHT, wavelength








.. GENERATED FROM PYTHON SOURCE LINES 21-26

A standing wave in front of a reflector
---------------------------------------

Incident and reflected waves add to :math:`2\sin(kx)\cos(\omega t)`;
nodes are half a wavelength apart.

.. GENERATED FROM PYTHON SOURCE LINES 26-37

.. code-block:: Python


    f = 450e6
    lam = float(wavelength(f))
    x = np.linspace(0, 3, 3001)
    envelope = np.abs(2 * np.sin(2 * np.pi * x / lam))
    interior = (envelope[1:-1] < envelope[:-2]) & (envelope[1:-1] < envelope[2:])
    nodes = x[1:-1][interior]
    spacing = np.mean(np.diff(nodes))
    print(f"f = {f / 1e6:.0f} MHz: node spacing {spacing:.4f} m -> speed {2 * spacing * f:.4e} m/s (c = {SPEED_OF_LIGHT:.4e})")
    assert np.isclose(2 * spacing * f, SPEED_OF_LIGHT, rtol=2e-3)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    f = 450 MHz: node spacing 0.3331 m -> speed 2.9981e+08 m/s (c = 2.9979e+08)




.. GENERATED FROM PYTHON SOURCE LINES 38-40

Wavelengths across the radio spectrum
-------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 40-52

.. code-block:: Python


    bands = {"LF 100 kHz": 1e5, "AM 1 MHz": 1e6, "FM 100 MHz": 1e8, "Hertz 450 MHz": 4.5e8, "Wi-Fi 2.4 GHz": 2.4e9, "Ku 12 GHz": 1.2e10}
    fig, axes = plt.subplots(1, 2, figsize=(10, 3.5))
    axes[0].plot(x, envelope)
    axes[0].plot(nodes, np.zeros_like(nodes), "kv")
    axes[0].set(xlabel="distance from reflector [m]", ylabel="field amplitude", title=f"Standing wave, λ = {lam:.3f} m")
    axes[1].barh(list(bands), wavelength(np.array(list(bands.values()))))
    axes[1].set_xscale("log")
    axes[1].set(xlabel="wavelength [m]")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/communications/propagation/images/sphx_glr_plot_01_hertz_wavelength_001.png
   :alt: Standing wave, λ = 0.666 m
   :srcset: /api/gallery/communications/propagation/images/sphx_glr_plot_01_hertz_wavelength_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.272 seconds)


.. _sphx_glr_download_api_gallery_communications_propagation_plot_01_hertz_wavelength.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/communications/propagation/plot_01_hertz_wavelength.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_hertz_wavelength.ipynb <plot_01_hertz_wavelength.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_hertz_wavelength.py <plot_01_hertz_wavelength.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_hertz_wavelength.zip <plot_01_hertz_wavelength.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_