what must be the height of the antenna if 3100Hz signal is tranmitted?

Answer 1

For .31 MHz, the half wavelength is 1500 ft

using the antenna length calculator in
http://www.crompton.com/wa3dsp/hamradio/antcalc.html

or
http://www.csgnetwork.com/antennaevcalc.html

I think your carrier frequency is too low
For 3.1 MHz it is 150 ft
for 31 Mhz it is 15 feet