# Connexions

You are here: Home » Content » Plane Waves

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

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?

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

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• Rice Digital Scholarship

This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Waves and Optics"

"This book covers second year Physics at Rice University."

Click the "Rice Digital Scholarship" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

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

# Plane Waves

Module by: Paul Padley. E-mail the author

Summary: A simple expression for a plane wave

## Plane Waves

We want to find the expression for a plane that is perpendicular to k k , where k k is a vector in the direction of propagation of the wave.The plane is the set of points that has the same projection onto the vector k k That is any point r r that satisfies k r = c o n s t a n t k r = c o n s t a n t is a point on the planeNow consider the function ψ ( r ) = A e i k r ψ ( r ) = A e i k r we see that the magnitude of ψ ( r ) ψ ( r ) is the same over every plane that is defined by k r = c o n s t a n t k r = c o n s t a n t we want to construct harmonic waves, ie. they should repeat every wavelength along the direction of propagation so they should satisfy ψ ( r ) = ψ ( r + λ k k ) ψ ( r ) = ψ ( r + λ k k ) where λ λ is the wavelengththen we must have A e i k r = A e i k ( r + λ k k ) = A e i k r e i k k λ / k = A e i k r e i k λ A e i k r = A e i k ( r + λ k k ) = A e i k r e i k k λ / k = A e i k r e i k λ This is true if e i λ k = 1 = e i 2 π e i λ k = 1 = e i 2 π or λ k = 2 π λ k = 2 π k = 2 π λ k = 2 π λ This should have a familiar look to it! Finally we want these waves to propagate in time so you should be able to guess the answer from our work on mechanical waves ψ ( r ) = A e i ( k r ω t ) ψ ( r ) = A e i ( k r ω t )

## Content actions

### 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

##### Lenses

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?

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