Fundamentals (Waves)

One-dimensional wave equation, wave speed, temporal frequency, and spatial wavelength.

General idea of the topic

This topic builds the basic language of waves. It defines what a wave disturbance is, how it is represented mathematically, and which quantities describe it.

What you will truly understand

You will understand the difference between amplitude, phase, frequency, period, wavelength, and speed. You will also see why the wave equation expresses a physical relation between spatial variation and temporal variation.

Recommended learning route

Start with the concept of a wave. Continue with the wave equation and wave quantities. Then classify waves according to their nature and according to the direction of the disturbance.

Physical criterion you must acquire

You should learn to identify which physical variable oscillates and which relation makes it propagate. Before using formulas, you must know whether the problem concerns a string, a pressure, a field, or a deformation.

Connection with real problems

The fundamentals are used in sound, optics, vibrations, seismic waves, communications, materials, and any system where a disturbance propagates.

Final goal of the topic

The final goal is to have a common physical and mathematical vocabulary for interpreting any later wave topic without relying on isolated recipes.