The **key difference between wavefront and wavelet** is that wavefront is the locus of all the points that are joining together with the same phase, a line, or a curve in a 2D medium, whereas a wavelet is a wave-like oscillation having an amplitude that is expanding and contracting gradually and sequentially.

Although the terms wavefront and wavelet sound similar, they are two different terms having different applications in physics.

### CONTENTS

1. Overview and Key Difference

2. What is Wavefront

3. What is Wavelet

4. Wavefront vs Wavelet in Tabular Form

5. Summary

## What is Wavefront?

Wavefront is the set of all points where a wave has the same phase of the sinusoid. This term is described regarding the wavefront of a time-varying field. Therefore, this term is generally meaningful only with fields that vary sinusoidally in time with a single temporary frequency at each point of the field. In other words, wavefronts usually move with time, and wavefronts are typically single points for waves that are propagating in a unidimensional medium. In 2D mediums, they are curves, while in 3D mediums, they are surfaces.

When considering a sinusoidal plane wave, the wavefronts can be defined as planes that are perpendicular to the direction of propagation which tends to move in that direction along with the wave. In a sinusoidal spherical wave, the wavefronts are spherical surfaces that tend to expand with the wave. Moreover, if the speed of the propagation of a wavefront is different at different points, then the shape and orientation of the wavefronts can be changed by refraction. For example, lenses can change the shape of optical wavefronts from planar to spherical (or sometimes vice versa).

## What is Wavelet?

Wavelets are wave-like oscillations having an amplitude that is beginning at zero, gradually increasing and decreasing back to zero. Typically, we can visualize it as a brief oscillation similar to the oscillations recorded by a seismograph or a heat monitor.

Furthermore, a wavelet can be formed to have a frequency that is Middle C and having a short duration of about 1/10^{th} of a second. If we can convolve this wavelet with a signal that is being created from a melody, this results in a signal that is useful in determining when the Middle C note is played during a song. This correlation is a practical application of wavelet theory.

The wavelet theory can be applied to several subjects because the transforms of wavelets appear as forms of time-frequency representations for analog signals, and they are also related to harmonic analysis.

There are different types of wavelets, including discrete wavelets (such as Beylkin, Coiflet, Haar wavelet, Symlet, etc.) and continuous wavelets (such as beta wavelet, Meyer wavelet, Mexican hat wavelet, Spline wavelet, etc.).

## What is the Difference Between Wavefront and Wavelet?

Although the terms wavefront and wavelet sound similar, they are two different terms having different applications in physics. The key difference between wavefront and wavelet is that wavefront is the locus of all the points that are joining together with the same phase, a line or a curve in a 2D medium, whereas a wavelet is a wave-like oscillation having an amplitude that is expanding and contracting gradually and sequentially.

The following table summarizes the difference between wavefront and wavelet.

## Summary – Wavefront vs Wavelet

Wavefront is the set of all points where a wave has the same phase of the sinusoid. Wavelets are wave-like oscillations having an amplitude that is beginning at zero, gradually increasing and decreasing back to zero. The key difference between wavefront and wavelet is that wavefront is the locus of all the points that are joining together with the same phase, a line or a curve in 2D medium, whereas a wavelet is a wave-like oscillation having an amplitude that is expanding and contracting gradually and sequentially.

##### Reference:

1. “Wavelet.” *An Overview | ScienceDirect Topics*.

##### Image Courtesy:

1. “Lens and wavefronts” By Oleg Alexandrov – self-made with MATLAB (Public Domain) via C0mmons Wikimedia

2. “Seismic Wavelet” By Joshua Doubek – Own work (CC BY-SA 3.0) via Commons Wikimedia

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