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

[woaini]

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?

 

[CWatters]

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.

 

[woaini]

How do I know how any nodes and antinodes to draw?

 

[CWatters]

The problem states "lowest electrical resonance"

 

[woaini]

Does that mean n=1?

 

[CWatters]

It says to treat it like a tube with closed ends. Closed ends on a tube form a node, open ends an anti node.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/clocol.html

 

[woaini]

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?

 

[CWatters]

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.

 

[woaini]

So how do I determine the formula for something closed on both ends?

 

[CWatters]

"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.

 

[woaini]

Oh I see, the formula should be f=v/2L

 

[woaini]

22220000m/s is the new speed I get?

 

[CWatters]

Remember they ask for a ratio.

 

[woaini]

Alright makes sense now.