How to determine the frequency of EM wave which does not oscillate?

[k9b4]

If I have a charge in a vacuum, and I accelerate it in a direction, then stop accelerating it, an EM wave will be produced for a short amount of time.

How can you determine the frequency of the EM wave which is produced? Does it depend on the speed at which the charge moves? The amount the charge accelerates?

 

[Dale]

You would use the Fourier transform. It would contain an infinite number of frequency components.

 

[Andy Resnick]

How can you determine the frequency of the EM wave which is produced? Does it depend on the speed at which the charge moves? The amount the charge accelerates?

There are at least three different mechanisms, each producing their own characteristic spectra. Bremsstrahlung is produced by accelerations associated with collisions:

http://en.wikipedia.org/wiki/Bremsstrahlung

Synchotron (or cyclotron) radiation is associated with electrons traveling through magnetic fields:

http://en.wikipedia.org/wiki/Synchrotron_radiation

Both of those have broad-band spectral distributions and can be characterized by routine measurement methods.

Free-electron lasers operate similarly to synchotron sources, but the magnetic field is spatially tuned (a 'wiggler') to provide a resonant interaction, resulting in narrow-band emission:

http://en.wikipedia.org/wiki/Free-electron_laser

 

[k9b4]

You would use the Fourier transform. It would contain an infinite number of frequency components.

Could you elaborate? What property of the charge is important in this Fourier transform? Is it the rate of acceleration of the charge?

 

[Dale]

Here is a link to the Wikipedia on the Fourier transform:
http://en.wikipedia.org/wiki/Fourier_transform

The Fourier transform is how you decompose any wave into its various frequency components. It has nothing specific to do with charge. It applies for EM waves, water waves, sound waves, and any other kind of waves you could imagine.