iMacs use the tones to indicate a hardware problem - it could be firmware or memory. The pattern of the tones is important - how many between pauses. Can you describe that?

Have you installed or removed RAM/Memory recently?

Its memory has failed an integrity check and probably needs to be replaced.

Memory is user-replaceable, and most reputable manufacturers have a lifetime guarantee. If it's the original Mac's memory, and no longer eligible for AppleCare, you might have to pay to replace it but memory is not terribly expensive.

Read here to determine how to replace it:

iMac (Late 2009) and later: Installing or replacing memory

Before giving up on it try removing and re-seating the modules.

Buy memory from OWC / MacSales or Crucial.

Intel-based Macs: Resetting the System Management Controller (SMC)

Note: It is possible that the SMC could encounter an issue that may cause  unusual system behavior typically related to the symptoms described  below.  In some cases, resetting the SMC may be the only correct method  to resolve the issue, however, an SMC reset should only be attempted  after all other standard troubleshooting has been performed.

Before Resetting the SMC

Try each of the following steps in this order before you reset the SMC.  Test the issue after completing each troubleshooting step to determine if the issue still occurs.

1. Press Command + Option + Escape to force quit any application that is not responding.
2. Put your Mac to sleep by choosing the Apple () menu from the upper-left menu bar and then choosing Sleep.  Wake the computer after it has gone to sleep.
3. Restart your Mac by by choosing the Apple () menu from the upper-left menu bar and then choosing Restart.
4. Shut down your Mac by by choosing the Apple () menu from the upper-left menu bar and then choosing Shut Down.

If your Mac appears to be running normally but isn't responding, force the computer to shut down by pressing and holding the power button for 10 seconds. Note: You will lose any unsaved work in any open applications.

For Mac portables experiencing issues related to the MagSafe power adapter and/or battery, try:

1. Unplug the MagSafe power adapter from the Mac and the wall power socket for several seconds.
2. Shutdown the Mac.  Physically remove and re-insert the battery (if it's removable) and startup the Mac.

If the issue is still not resolved after following the troubleshooting items above, an SMC reset may be necessary.

After performing normal troubleshooting, these symptoms may indicate that an SMC reset may be necessary:

Fans
The computer's fans run at high speed although the computer is not experiencing heavy usage and is properly ventilated.

Lights
The keyboard backlight appears to behave incorrectly (on Mac computers that have this feature).
The Status Indicator Light (SIL) appears to behave incorrectly (on Mac computers that have an SIL).
Battery indicator lights, if present, appear to behave incorrectly (on portables that use non-removable batteries).
The display backlight doesn't respond correctly to ambient light changes on Mac computers that have this feature.

Power
The computer doesn't respond to the power button when pressed.
A portable Mac doesn't appear to respond properly when you close or open the lid.
The computer sleeps or shuts down unexpectedly.
The battery does not appear to be charging properly.
The MagSafe power adaptor LED doesn't appear to indicate the correct activity.

System Performance
The computer is running unusually slowly although it is not experiencing abnormally high CPU utilization.

Video
A computer that supports target display mode does not switch into or out of target display mode as expected.
A computer that supports target display mode switches into or out of target display mode at unexpected times.