Skip to content Skip to navigation


You are here: Home » Content » Phasors: Numerical Experiment (Interference Patterns)


Recently Viewed

This feature requires Javascript to be enabled.


(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Phasors: Numerical Experiment (Interference Patterns)

Module by: Louis Scharf. E-mail the author

Note: You are viewing an old version of this document. The latest version is available here.

Let's add two sinusoids whose amplitudes and frequencies are identical and whose phases are different:

x ( t ) = A cos ( ω t + φ ) + A cos ( ω t + φ + ψ ) . x ( t ) = A cos ( ω t + φ ) + A cos ( ω t + φ + ψ ) .

Show analytically that this sum has the phasor representation

X = 2 A c o s ( ψ 2 ) e j [ φ + ( ψ / 2 ) ] . X = 2 A c o s ( ψ 2 ) e j [ φ + ( ψ / 2 ) ] .

Interpret this finding. Then write a MATLAB program that computes and plots complex X on the complex plane as ψ varies from 0 to 2π2π and that plots magnitude, |X||X|, and phase, arg X argX, versus the phase angle ψ ψ. (You will have to choose ψ=n2πN,n=0,1,...,N-1ψ=n2πN,n=0,1,...,N-1, for a suitable N.N.) When do you get constructive interfelence and when do you get destructive interference? Now compute and plot x(t)x(t) versus t t (you will need to discretize t t) for several interesting values of ψ ψ. Explain your interference results in terms of the amplitude and phase of x(t)x(t) and the magnitude and phase of X X. Use the subplots discussed in Appendix 1 to plot all of your results together.

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens


A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks