# Questions regarding design problem

My instructor in electrical circuits has given me the following creative problem:

Construct a communication chain, that follows the drawing below: The input is an AM signal, $$\V_{send}=V_1\cdot cos(2\pi f_1t)+V_2\cdot cos(2\pi f_2t)\$$

The chain consists of:

$$\V_{send}\$$ $$\\rightarrow\$$ An amplifier $$\\rightarrow\$$ Transmitter antenna $$\\rightarrow\$$ Transmission through air with distance $$\d\$$ $$\\rightarrow\$$ Receiving antenna $$\\rightarrow\$$ An amplifier $$\\rightarrow\$$ $$\V_{rec}\$$

Plot the frequency spectrum of $$\V_{rec}\$$.

Okay, for this I have some questions.

1. I plan to use the HA-8089 antenna as my transmission antenna, but can I also use it as my receiving antenna, or do I need another antenna for that?
2. Are the amplitudes and frequencies in $$\V_{send}\$$ (by those I mean $$\V_1\$$,$$\V_2\$$,$$\f_1\$$,$$\f_2\$$) dependent of what antenna or amplifier I use, or can I choose the values as I like?
3. When the signal travels through the air, it gets damped. To calculate the dampening I intend to use this formula: $$\F=20log(d)+20log(f)+32.44−Gtx−Grx\$$. Where $$\f\$$ is the frequency and $$\Gtx\$$, $$\Grx\$$ are the gains for the transmitting and receiving antenna. But what frequency should I use? $$\f_1\$$, $$\f_2\$$, or a combination of the two?
4. And lastly: When I have the amplifier gains, the antenna gains and the signal dampening, how do I then combine all that information to calculate the received signal, $$\V_{rec}\$$? Would it just be: $$\V_{rec}=(V_{send}\cdot G_{amp} \cdot G_{trans} -dampening) \cdot G_{rec} \cdot G_{amp}\$$?

I know that was a lot of questions, but I need some help now, cause I haven't been able to find an answer.