What is the minimum freqeuncy required to transmit 2400 bits per second?
Channel capacity is:

\$ C = B \log_2 (1+\frac{S}{N}) \$


\$B\$ is the channel bandwidth
\$\frac SN\$ is the signal to noise ratio or SNR


So, you can push 2400bps through a channel with a lower bandwidth than 2400bps, depending on coding, and of course depending on SNR.

For example, if B = 240Hz, then you will need a S/N ratio of 1023, or about 30dB, which is feasible on short copper cables. 

A simplistic code to achieve this would be to assemble the bits into 10-bit symbols, translate this into a voltage between 0 and 1024V, and use a channel with noise lower than 1V.

Gigabit Ethernet does not use 1GHz bandwidth...