Searching disk images

I use writable, encrypted disk images to protect private files and data on my MBP. I mount the drive to work with the files and close them again when I'm done.

One thing has always been a nuisance, however, any kind of search through the data, yields no results. This is the related info for one of the dmg files.

File system : Mac OS Extended (Journaled)

Connection : Disk Image

Device tree path : IODeviceTree:/

Writable : Yes

Is case-sensitive : No

Volume capacity : 65,000,001,536

Available space (Purgeable + Free) : 23,323,787,264

Owners enabled : No

Is encrypted : Yes

System Integrity Protection supported : No

Can be verified : Yes

Can be repaired : Yes

Bootable : No

Journaled : Yes

S.M.A.R.T. status : Not Supported

Would appreciate any suggestions. Thanks