Whene I am using the computer and open an application there is some kind of beeping noise and continues off and on while I have the applications open.  It doesn't do it until I open something and it doesn't matter what it is.  I have WXP w/a Pentium 4 processor.  Would anyone have any idea what would cause this?  Any suggestons will be appreciated.

Only a few things I can think of creating beeps when actually running,
1 - an overheating condition to CPU, thermal may be activated,
2 - (only seen this a few times) beeping coming from hard disk, also due to overheating.

Check your PC Health in BIOS after a reboot, check CPU and System temperature there.

I agree with Zedy. Get a can of compressed air. Open up your ( shutdown  ) PC and carefully blow out your dust bunnies concentrating on your CPU cooler, Hard drives and fans. Do not let this continue as you could have serious problems leading to data loss.

   I would think that it is a problem with the sound card.  Maybe the sound card is bad.