Basic Waves: Theory and Interactive Simulation

A wave is a phenomenon of energy transfer from one point to another through oscillation or vibration, without the medium moving along with the wave (such as water waves, sound waves), or in some cases, waves can travel without a medium (such as light waves). Waves are highly important in engineering, ranging from designing earthquake-resistant structures to wireless telecommunication systems.

Interactive Wave Simulation

You can try changing the numbers in the boxes below to observe how Amplitude, Wavelength, and Frequency affect the shape and speed of the wave.

Key Wave Properties

For simpler understanding, we often consider waves in the form of Sine Waves, which have key variables used to describe the characteristics of the wave as follows:

• Amplitude ($A$): The maximum displacement from the equilibrium position (the height of the wave crest). A wave with high amplitude carries more energy. In the case of sound waves, a higher amplitude means a louder sound. It is measured in meters (m).
• Wavelength ($\lambda$): The shortest distance between 2 points that have the same oscillation state (phase), such as measured from one crest to the next. It is measured in meters (m).
• Frequency ($f$): The number of cycles the wave travels past a point of observation in one unit of time. It is measured in Hertz (Hz) or cycles per second.
• Period ($T$): The time it takes for the wave to travel past an observation point for 1 full cycle. It is inversely proportional to frequency ($T = 1/f$). It is measured in seconds (s).
• Wave Speed ($v$): The speed at which wave energy travels forward. It can be found from the product of frequency and wavelength ($v = f \times \lambda$). It is measured in meters per second (m/s).