Fundamental Wavelength of Vibration of Steel Wire 1m Apart

In summary, the fundamental wavelength of vibration of a steel wire stretched taut between supports one meter apart can be defined as the longest wavelength with a node at the two poles. In order for the wire to have a wavelength of 1 meter, it would need to have some slack, but it is possible for the wire to have arbitrarily small wavelength waves.
  • #1
tandoorichicken
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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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  • #2
Begin by defining "fundamental."

- Warren
 
  • #3
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.
 
  • #4
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.
 
  • #5
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").
 

FAQ: Fundamental Wavelength of Vibration of Steel Wire 1m Apart

What is the fundamental wavelength of vibration of a steel wire 1m apart?

The fundamental wavelength of vibration of a steel wire 1m apart is the shortest distance between two consecutive points on the wire that are in phase with each other. In other words, it is the distance between two points where the wire is vibrating with the same amplitude and direction.

How is the fundamental wavelength of vibration of a steel wire 1m apart determined?

The fundamental wavelength of vibration can be determined using the formula λ = 2L/n, where λ is the wavelength, L is the length of the wire, and n is the number of nodes (points of no vibration) between the two ends of the wire. For a steel wire 1m apart, n would be equal to 2, since there is a node at each end.

Does the material of the steel wire affect the fundamental wavelength of vibration?

Yes, the material of the steel wire can affect the fundamental wavelength of vibration. Different materials have different densities and stiffness, which can impact the speed at which vibrations travel through the wire. This can result in a different fundamental wavelength of vibration for different materials.

How does tension affect the fundamental wavelength of vibration of a steel wire?

Tension can have a significant impact on the fundamental wavelength of vibration of a steel wire. The higher the tension, the faster the vibrations will travel through the wire, resulting in a shorter wavelength. Conversely, lower tension will result in a longer wavelength.

Why is the fundamental wavelength of vibration of a steel wire 1m apart important?

The fundamental wavelength of vibration of a steel wire is important because it is a fundamental property of the wire that can have implications for its performance in various applications. It can also provide valuable information about the material and its physical properties, such as density and stiffness.

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