Microscopy Primer
Light and Color
Microscope Basics
Special Techniques
Digital Imaging
Confocal Microscopy
Live-Cell Imaging
Microscopy Museum
Virtual Microscopy
Web Resources
License Info
Image Use
Custom Photos
Site Info
Contact Us

The Galleries:

Photo Gallery
Silicon Zoo
Chip Shots
DNA Gallery
Amino Acids
Religion Collection
Cocktail Collection
Screen Savers
Win Wallpaper
Mac Wallpaper
Movie Gallery

Interactive Java Tutorials

Complex Waveforms and Beat Frequencies in Superposed Waves

In general, the process of describing interference through the superposition of sine waves generates simple waveforms that can be adequately represented by a resultant sine curve in a plot of amplitude, wavelength, and relative phase displacement. If the recombined waves have appreciably different frequencies, the resulting waveform is often complex, yielding a contour that is no longer a sine function with a simple, single harmonic. This interactive tutorial explores the complex waveforms and beat frequencies generated by the superposition of two light waves propagating in the same direction with different relative frequencies, amplitudes, and phases.

Interactive Java Tutorial
Our servers have detected that your web browser does not have the Java Virtual Machine installed or it is not functioning properly. Please install this software in order to view our interactive Java tutorials. You may download the necessary software by clicking on the "Get It Now" button below.


The tutorial initializes with two parallel light waves, labeled Wave 1 and Wave 2, assumed to be propagating parallel to each other from left to right in the two upper frames of the tutorial window. The resultant wave arising from the summation of the two waves by interference is presented as the Wave Sum in the bottom-most frame of the tutorial window. In order to operate the tutorial, use the Wavelength, Phase, and Amplitude sliders to vary these parameters for each of the input waves, and observe how the resultant wave is affected.

In cases where the superposed waves have closely matched wavelengths and amplitudes (for example, 400 and 430 nanometers), the resultant waveform displays several harmonics, including the classical beat frequencies so commonly observed in sound waves. This effect was first demonstrated with light waves in 1955, prior to the invention of the laser, and is quite useful in a number of applications, including the Doppler effect that accounts for the frequency shift when light is reflected from a moving surface. A precise measure of the speed of an object can be derived by scattering light from the target, and then beating the original and reflected waves.

Adding together two waves that have significantly different wavelengths (400 and 650, for example) produces complex waveforms that deviate significantly from a simple sine function. If the resultant wave is composed of visible light, the human eye experiences the sensation of a mixture of two colors, which are the same regardless of the phase difference. The examples presented in the tutorial are monochromatic in nature, but white light can be considered as an extreme case of superposition between waves, where a large number of simple waveforms have wavelengths that differ by only a few nanometers. In this case, Fourier analysis is necessary to describe the complex interplay that occurs between waveforms in such a composite mixture of wavelengths.

Contributing Authors

Robert T. Sutter and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.



Questions or comments? Send us an email.
© 1998-2013 by Michael W. Davidson and The Florida State University. All Rights Reserved. No images, graphics, scripts, or applets may be reproduced or used in any manner without permission from the copyright holders. Use of this website means you agree to all of the Legal Terms and Conditions set forth by the owners.
This website is maintained by our
Graphics & Web Programming Team
in collaboration with Optical Microscopy at the
National High Magnetic Field Laboratory.
Last modification: Wednesday, Mar 26, 2014 at 02:23 PM
Access Count Since February 21, 2003: 32056
For more information on microscope manufacturers,
use the buttons below to navigate to their websites: