When your MacBook Air beeps intermittently, and you've ruled out notification sounds from email and chat programs, it's generally a warning of errors of some kind. These errors can range from simple, temporary errors to severe hardware problems that require repair by Apple technicians. The MacBook Air sacrifices accessibility for convenience, so you can't open it up to fix anything yourself. You can perform troubleshooting to narrow down the problem or fix it yourself, but back up your data before anything else to avoid losing important work.
System Management Controller Needs Reset
The System Management Controller is responsible for your MacBook's operating temperature, fan speed and power flow. It normally runs fine and does not need any input from the user. If the SMC does need to be reset, or if some error associated with it causes your MacBook to overheat, you can reset it with a short process. Shut down your computer completely and then plug in the power cable if it is not already plugged in. Hold down "Left Shift | Control | Option | Power button" simultaneously. Hold for five seconds and then release. Press the power button again to turn on your computer to see if it worked.
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NVRAM Needs Reset
NVRAM contains user-setting information such as speaker volume, screen resolution and default startup disk selection. If there are any temporary issues with any of these settings, your MacBook's NVRAM can be reset using a similar method to resetting the SMC. Power down your computer completely. Press the power button to turn on the computer again, then immediately press and hold the "Command | Option | P | R" keys simultaneously. Continue holding them until the computer restarts or you hear the startup sound a second time.
Occasionally a program running in the background may cause intermittent beeping noises. One way to check this is by muting your MacBook's speakers to see if you can still hear the sound; system error beeps override the volume controls, so if there is any serious hardware issue, you will still hear sound. If not, check all your running programs and processes to see if anything that is running could cause the beeping. To check a full list of all open programs and processes, open the "Applications" folder, select the "Utilities" subfolder and open "Activity Monitor."
Hardware Error or Failure
In the event of a serious hardware or system error, your MacBook beeps to let you know of the error -- hopefully, before anything serious occurs. The beeping can mean a hard drive failure or unseated RAM. If you have tried all other troubleshooting steps and the beeping still occurs, take the MacBook to an Apple Store or contact support if there are no stores nearby. Taking apart your laptop to attempt to fix it yourself may void your warranty. In the meantime, take precautions and back up all your data to an external hard drive, another computer or the cloud.