I have Seagate 2 TB external Hard drive(Seagate Backup Plus Slim, to be exact). When I connect it to USB 2.0 port or eSATA port, it gets started spinning and beeps 2 times. Then it keep spinning for some time. Then it gets stopped. The light doesn't glow anywhere during the process. The hard drive is just 2 months old. Also I tested it on both Ubuntu and Windows 7 and on different laptops.
When I connect it to USB 2.0 or eSATA port, it starts spinning and beeps 2 times.
It is possible that your drive is not getting enough power:
Seagate and Maxtor-brand hard drives do not contain audio speakers. Some failure mechanisms may make a regular repeating beep from the computer's internal speaker. This may or not be hard drive related.
Check your system documentation for an explanation of system beep codes. If a drive failure is possible, it is always important to make an immediate backup.
Troubleshooting noise issues for external drives:
External USB drive clicking and beeping can occur if the USB port does not provide enough power to operate the drive, often a USB 1.x port, or an unpowered USB hub. To resolve this noise, connect the drive with both of the USB connectors (if possible), or if your drive only has one connector, try connecting it to other USB ports on your computer. If that does not work, connect it to a powered USB hub to ensure enough electrical power.
The Seagate Portable, Seagate FreeAgent Go Classic, and Maxtor OneTouch mini drives, in particular, included a USB Y-cable with two USB connectors so that, if one USB port did not power the drive enough, it could be connected to a second USB port.