Disabling the system alert beep
There are 2 ways to disable the system beep/alert in Solaris:
1.) If you are using JDS desktop, do the following:
Launch --> Preferences --> Desktop preferences --> Sound --> system bell --> Uncheck Sound an audible system bell.
2.) From the command line, execute
/usr/openwin/bin/xset b 0
P.S: Thanks to Ananth Shrinivas of BOSUG for the educating me about the command line option!