Why Is the Frequency of the Standing Wave in the Wire 2f?

[teleport]

Homework Statement

This is more like a concept question.

If you have a solenoid with AC frequency f, placed in close proximity on top of a wire with both ends fixed, and projected parallel to it, why is the frequency of the standing wave observed in the wire equal to 2f?

The Attempt at a Solution

This is about magnetic forces and fields which I haven't studied yet. This is out of curiosity, after seeing that statement without any explanation in my last lab. Thank you if you can clear this for me.

 

[andrevdh]

The magnetic field of the solenoid causes the wire to become magnetized with an opposite polarity as that of the solenoid. This means that the wire will become a N and S pole near the solenoid during each cycle of the current in the solenoid. The wire will therefore be attracted by the solenoid twice during each cycle of the current.

 

[teleport]

Thanks. When you mean cycle, do you refer to current going through one coil, or going through the entire solenoid? (I think only one coil) Also, at what moments will the polarity in the solenoid change, thus inducing two magnetic forces on the wire per cycle? Thanks a lot.

 

[andrevdh]

Since the solenoid is one continuous piece of wire the current through it will be the same "everywhere" in it.

Normally we use the right hand rule to determine the direction of the magnetic field : Curl the fingers of the right hand in the direction of conventional current flow in the coil. The thumb will then point in the direction of the magnetic field lines. This means that the field changes direction when the current changes direction (E and B fields are in phase). The induced magnetism will normally lag behind in time due to the fact that it takes a finite amount of time for the magnetic domains to orientate themselves (this is also true for the solenoid - a delayed effect).

 

[teleport]

o I think I get it now. Great. Thank you.