Let us consider the case of a satellite dish receiving a TV signal from a satellite at 11.75 GHz. You cannot use an inexpensive coaxial cable to bring this microwave frequency into the building but instead you would need what is called a "waveguide". Also as mentioned at https://en.wikipedia.org/wiki/Intermediate_frequency, "at very high (gigahertz) frequencies, signal processing circuitry performs poorly. Active devices such as transistors cannot deliver much amplification (gain). Ordinary circuits using capacitors and inductors must be replaced with cumbersome high frequency techniques"
For these reasons, it is necessary to convert a given frequency to a different frequency, an "intermediate frequency" as it is called. For satellite TV the intermediate frequency used is in the range of 950 - 2150 MHz.
The AM radio band is from 535 to 1605 kHz. In other words, the Amplitude Modulated (AM radio) carrier frequencies are in the frequency range 535-1605 kHz. (Note:
carrier frequencies of 540 to 1600 kHz are assigned at 10 kHz intervals.) The FM radio band is from 88 to 108 MHz.
The intermediate frequency used in AM radio is 455 kHz. For FM radio it is 10.7 MHz.
Image reference: http://hyperphysics.phy-astr.gsu.edu/hbase/Audio/radio.html
Generation of new frequencies at sum or difference of original ones - Represented mathematically with wave multiplication
What is the result of applying two different voltages (cf. waveforms) on a non-linear electrical circuit element like a diode?
“RF mixing is not like audio mixing where several signals are added together in a linear fashion to give several sounds together. Radio frequency, or RF mixing is a non-linear process that involves the instantaneous level of one signal affecting the level of the other at the output.”
“It is found that if two signals are passed through a non-linear circuit, then additional signals on new frequencies are formed. These appear at frequencies equal to the sum and difference frequencies of the original signals. In other words if signals at frequencies of f1 and f2 enter the mixer, then additional signals at frequencies of (f1+f2) and (f1-f2) will also be seen at the output.”
(1) “If two signals, one at a frequency of 5 MHz and another at a frequency of 6 MHz are mixed together then new signals at frequencies of 11 MHz and 1 MHz are generated.”
“RF mixer mathematics: It is possible to easily represent the action of an RF mixer mathematically. The two input waveforms are represented by simple sine waves, and these are multiplied together.” (cf image of post)
(2) RF Mixer applications: “They are used in circuits from radio receivers and transmitters to radar systems”
"Frequency translation: The most obvious application for RF mixers is for frequency translation. This technique is used in many areas and in particular in receivers and transmitters to move the frequency of a signal from one band to another."
Additional reference: https://en.wikipedia.org/wiki/Frequency_mixer