Does iPad 3rd generation support dual band wi-fi ?

No.

IPad 3

Wireless and Cellular

Wi-Fi

• Wi-Fi (802.11a/b/g/n)
• Bluetooth 4.0 technology

Wi-Fi + Cellular

• Wi-Fi (802.11a/b/g/n)
• Bluetooth 4.0 technology
• Model for AT&T: 4G LTE (700, 2100 MHz)3; UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)
• Model for Verizon: 4G LTE (700 MHz)3; CDMA EV-DO Rev. A (800, 1900 MHz); UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)
• Data only4

I believe that Kappy's response is accurate, here is the same spec for the ipad air, notice the differences.

Ipad Air

Wi-Fi

• Wi-Fi (802.11a/b/g/n); dual channel (2.4GHz and 5GHz) and MIMO
• Bluetooth 4.0 technology

Wi-Fi + Cellular

• Wi-Fi (802.11a/b/g/n); dual channel (2.4GHz and 5GHz) and MIMO
• Bluetooth 4.0 technology
• GSM/EDGE
• CDMA EV-DO Rev. A and Rev. B
• UMTS/HSPA/HSPA+/
  DC-HSDPA
• LTE⁴
• Data only⁵

If it supported dual-band, then it would say so in the specs as it does for the iPad Air which is the first model to support dual-band.

My iPad 2 connects to both 2.4 & 5GHz. So your iPad 3 should also. However, the 5GHz band has a shorter range compared to 2.4GHz.

Does your iPad 3 recognize both bands, but not connect to 5GHz?

 Cheers, Tom 😉

Look at this link. http://blogs.aerohive.com/blog/the-wireless-lan-architecture-blog-3/ipad-3-wi-fi -performance-analysis-throughput