What Causes Superimposition in String Fundamentals and Standing Waves?

AI Thread Summary
In the fundamental mode of a vibrating string, the two impulses superimpose to create a standing wave, with the fixed ends determining the wavelength. The fundamental frequency corresponds to the longest wavelength, where the distance between the fixed ends equals the distance between two adjacent nodes, which is half a wavelength. Standing waves also occur in electrical signals, where they propagate through a channel and reflect back, achieving maximum transmission when the forward-to-reflected signal ratio is 1:1. The discussion raises questions about the physical boundaries of acoustic waves and their reflection. Understanding these principles is key to grasping wave behavior in both mechanical and electrical systems.
lektor
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This is not homework question but more of a personal interest question.

Can anyone help explain why it is that in the fundamental of a string the 2 impulses superimpose to form:
 

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lektor said:
This is not homework question but more of a personal interest question.

Can anyone help explain why it is that in the fundamental of a string the 2 impulses superimpose to form:
The position of the fixed ends of the string determines the wavelength. The fundamental is the longest wavelength of vibration for which the distance between fixed ends is the distance between two adjacent nodes. Any longer wavelength would require the fixed end of the string to move. The distance between two adjacent nodes is 1/2 a wavelength.

AM
 
With a string, what is the standing wave, standing between? :rolleyes:

With electrical signals, standing waves occur within a channel (wire, optical fiber etc.). The signal actually propagates the length of the channel and then radiates back. Maximum signal is transmitted when the forward/reflected ratio is 1:1

Thinking about the standing wave graph (time vs amplitude) that lektor gave, does the acoustic wave propagate out to a boundary and reflect back again to its origin? Where would be the physical position of the origin and boundary? :rolleyes:
 

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