I was told I have a cavity under a fairly new crown. Can a cavity under a crown be detected through xray?

The answer to this question depends on the type of dental crown that you have.  Radiographically, you can't see through a crown that has a metal coping or is all metal.  An all porcelain restoration allows for the doctor to see through the crown and see the extent of any recurrent decay present.  Hope this helps.  

The answer can be yes or no depending on what the crown is made of, the location of the decay. Metal, porcelain to metal and zirconia crowns are radio-opaque and x-rays only show th margins and below. Frequently a small area of decay is picked up in examination before it is large enough to see on an x-ray.  The reason for regular examinations and periodic bite wings is to catch these small problems when they are easy to fix.  Most root canals and lost teeth are related to small problems being left to become large problems.

I agree with the other posters that it depends on the location and the type of material that the crown is made from.