Fundamental Wavelength of Vibration of Steel Wire 1m Apart

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Homework Help Overview

The discussion revolves around determining the fundamental wavelength of vibration of a steel wire that is stretched taut between two supports one meter apart.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of "fundamental" and its implications for wave behavior in a fixed wire. There are discussions about the conditions necessary for nodes and the relationship between wavelength and tension in the wire.

Discussion Status

Participants are actively engaging with the concepts, questioning assumptions about the nature of the wave and the conditions for nodes. Some clarification on the definition of fundamental wavelength has been initiated, and differing interpretations of wave behavior are being explored.

Contextual Notes

There is an ongoing discussion about the tension in the wire and the implications for the formation of nodes, as well as the definition of fundamental wavelength in this context.

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A steel wire is stretched taut between supports one meter apart. What is the fundamental wavelength of vibration of the wire?
 
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Begin by defining "fundamental."

- Warren
 
Since the wave is fixed at the two poles, the wave must have 0 value at those two points. The standard sine wave (wave length 2pi) is 0 at 0, pi, and 2pi. A wave of wave length l will be 0 at 0, l/2 and l. In particular, the longest wave (which I take is what you mean by "fundamental wavelength") that is 0 at 0 and 1 must have wavelength 2.
 
I get it, so the only way for it to have a wavelength of 1 m is if there was a node in the wire, and then it would have to have some slack, which it doesnt.

Thanks.
 
No, it is quite possible for the wire to have a node in the center without "slack" (it has to be under tension and able to stretch in order to form waves). You asked for the fundamentalwavelength which is the longest wavelength (lowest frequency). It is possible for the wire to have arbitrarily small wavelength waves ("harmonics").
 

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