Calculating Ratio of Electrical Current to Light Speed: A Challenge!

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Homework Help Overview

The problem involves calculating the ratio of the speed of electrical current in a wire to the speed of light, given a specific frequency and length of the wire. The context is set within the framework of electrical resonance and wave behavior in a closed tube.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between frequency, wavelength, and the length of the wire, questioning how to determine the wavelength and the mode of resonance. There is exploration of the implications of closed ends on the tube and how that affects the standing wave pattern.

Discussion Status

Participants are actively engaging with the problem, offering hints and clarifications about the standing wave patterns in tubes. There is some confusion regarding the correct formula for a closed tube, with multiple interpretations being explored. Guidance has been provided on how to visualize the problem and apply the correct equations.

Contextual Notes

There is an ongoing discussion about the assumptions regarding the mode of resonance and the implications of treating the wire as a tube with closed ends. Participants are also addressing the need for clarity on the number of nodes and antinodes in the context of the problem.

woaini
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Homework Statement



If a 0.505m long wire is excited into its lowest electrical resonance by a 2.2E7 Hz electrical oscillator, what is the ratio of the speed of the electrical current to that of light? Assume that the wire is like a tube with both ends closed.

f=2.2E7
L=0.505
v=?

Homework Equations



f=nv/2L
f=v/λ


The Attempt at a Solution



How do I solve this problem if I do not have λ or n? How would the equations work?
 
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Hint: How would you find λ if this was a problem involving sound waves in an organ pipe? You would do a drawing showing a standing wave with nodes and antinodes then calculate the wavelength.
 
How do I know how any nodes and antinodes to draw?
 
The problem states "lowest electrical resonance"
 
Does that mean n=1?
 
It says the fundamental frequency for a closed cylinder is f=v/4L

Therefore the speed I determine using the formula is...

v= f*4L = 2.2E7 * 4 *0.505 = 444400000 m/s

And the ratio of it to the speed of light is:

444400000 m/s / 3E8 m/s = 0.148

Does this look correct?
 
It says the fundamental frequency for a closed cylinder is f=v/4L

I think that's the formulae for a cylinder with one end open and one closed.
 
So how do I determine the formula for something closed on both ends?
 
  • #10
"Closed ends on a tube form a node..."

Draw it?

If you looked at the link I gave earlier it shows a drawing for one end open and one end closed. You can see how the formula is derived from that drawing. Do a new drawing with both ends closed and apply same ideas.
 
  • #11
Oh I see, the formula should be f=v/2L
 
  • #12
22220000m/s is the new speed I get?
 
  • #13
Remember they ask for a ratio.
 
  • #14
Alright makes sense now.
 

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