How do I find out or identify the speed of my memory (DIMM) through command prompt options under Linux operating systems? How do I find out speed of the DIMM’s using a shell prompt?

You can find out the speed using dmidecode or lshw command under any Linux distribution.

Install lshw

If you are using Debian / Ubuntu Linux, enter:
# apt-get install lshw
If you are RHEL / Fedora / Red Hat / CentOS Linux, enter the following after enabling EPEL repo:
# yum install lshw

How do I use lshw to display DIMM speed?

Type the command as follows:
# lshw -short -C memory
Outputs:

H/W path              Device     Class      Description
=======================================================
/0/0                             memory     108KiB BIOS
/0/4/6                           memory     16KiB L1 cache
/0/4/7                           memory     8MiB L2 cache
/0/5/8                           memory     16KiB L1 cache
/0/5/9                           memory     8MiB L2 cache
/0/16                            memory     12GiB System Memory
/0/16/0                          memory     2GiB DIMM Synchronous 667 MHz (1.5 ns)
/0/16/1                          memory     2GiB DIMM Synchronous 667 MHz (1.5 ns)
/0/16/2                          memory     2GiB DIMM Synchronous 667 MHz (1.5 ns)
/0/16/3                          memory     2GiB DIMM Synchronous 667 MHz (1.5 ns)
/0/16/4                          memory     2GiB DIMM Synchronous 667 MHz (1.5 ns)
/0/16/5                          memory     DIMM Synchronous 667 MHz (1.5 ns) [empty]
/0/16/6                          memory     2GiB DIMM Synchronous 667 MHz (1.5 ns)
/0/16/7                          memory     DIMM Synchronous 667 MHz (1.5 ns) [empty]

See how to use dmidecode to find out RAM speed and type under Linux.