Purpose of the program: (schools, colleges, universities, research centers)

The software complex “Wave geometry” is intended for research in the field of acoustics, electrodynamics and quantum mechanics, as well as for demonstration of wave phenomena and processes in simple and complex systems of wave-forming sources. The complex provides ample opportunities for the researcher to visualize the studied processes and obtain accurate parametric data.

The program is based on the Euclidean geometry, in which the missing axiom missed by Euclid is added to the known axioms: the axiom of the presence of the base (the axiom of the base). At its core, this axiom is a substrate (carrier) for displaying points, lines, shapes in both “frozen” and kinematic form.

Without carrier for builds (base), there is no way to display anything. The carrier can be one-dimensional, two-dimensional, and imaginary. The carrier is always motionless in relation to the external observer and is an absolute frame of reference.

Mathematical apparatus for the calculation and display of what is happening on the screen are algebra and trigonometry.

What the program will demonstrate:

  • Doppler effect (all variants at V=const);
  • Doppler effect during acceleration of "source-receiver" system (V=at);
  • Doppler effect at accelerated motion of either source or receiver, or both;
  • standing waves compression (length of the base, correction for phase);
  • speed of the energy current;
  • interference from two or more sources;
  • self-organization of two or more sources;
  • reaction of the source system to a change in parameters;
  • movement and self-movement of soft systems consisting of two or more sources;
  • movement and self-movement of rigid systems consisting of two or more sources;
  • distribution of kinetic and potential energy in the source system;
  • wave calculator that allows to automatically calculate all the geometric and wave parameters;

The user will be able to vary the parameters and observe the changes occurring both in the field of interfering waves and with the source system.

Doppler effect

  • user will be able to study/investigate the Doppler effect for all possible standard situations;
  • user will be able to study/investigate the Doppler effect for the situation of system motion with acceleration;
  • user will be able to set and receive data of wavelengths and frequencies of sources and receivers;

Standing waves compression

  • user will be able to study and compare the dependence of the standing wave length on the speed and orientation of the source system;


This functionality will allow you to construct interferometric devices and visualize the wave processes occurring in the device, as well as to predict the results. In the program, you can select the original postulates that underlie a particular physical model, and compare the results.

For example, the Michelson interferometer.

There are at least two conditions for analysis:

1) Existence of wave medium;

2) Absence of wave medium;

To study condition №1, three variants of coordinate transformations are selected: according to Galileo, according to Lorentz, according to Voigt. It will be possible to investigate the ballistic version proposed by Walther Ritz.

For option №2, in which the speed of waves is always constant relative to the radiating source, also you can view what is happening.

Basic formulas included in the program:

  • dependence of the wavelength on the source velocity (Doppler effect);
  • dependence of the received frequency on the speed of the source/receiver;
  • dependence of the standing wave length of an approaching/receding mirror/source;
  • dependence of the standing wave length in the source system on its velocity and orientation angle to the direction of motion;
  • dependence of the symmetry of the wave image in a moving system on the reduction of the system size and phase shift between the oscillating elements;

About the engineering component of the program

The program will provide an opportunity to study the properties of natural (floating) and artificial (rigid) structures of the active elements (wave sources) for certain parameters, as well as changes in these parameters.

For example, the property “inertness”, i.e. how and in what way this property arises in the system, as well as the property “motion by inertia”, i.e. how and due to what the system, being in an arbitrary speed mode, maintains a state of equilibrium of internal forces?

This feature will allow you to understand how to manage complex systems of active elements in order to get their reaction in the form of movement in the space of the wave medium.