Superposition of Standing Waves on a String

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The shapes of the first harmonics are shown for a vibrating string of length fixed at each end. The frequency of the fundamental mode of vibration is , where is the speed of the wave and the wave function is .

[more]

In general, a vibrating string does not vibrate in a single harmonic mode. The motion is a superposition of several harmonics. The wave function is a linear combination of harmonic functions , where and are constants determined by initial conditions of the problem. The initial shape of the string is shown in the lower plot when . It is symmetric about the point and initial velocity zero throughout the string. The movement of the string after being released is still symmetric with respect to . Only the odd harmonics ( odd) are excited. The even harmonics are null with .

[less]

Contributed by: Ronai Machado Lisboa (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send