I know that radiowaves from radiostations are modulated either F.M or A.M .

Lets suppose they are F.M and one has carrier wave frequency of 100 Hz and other 200 Hz they have F deviation of 20Hz/V .

Now suppose same information signal (Amplitude = 2V and frequency = 10Hz) is passed onto each station.

They both will have bandwith of (60-140 Hz) and (160-240 Hz) respectivly and these Frequencies will change 10 times in 1 second in both cases.

now interference requires constant phase difference and since in both cases frequencies change at same rate should'nt interference occur?

Which means if 2 radiostations have same song being played, should'nt the louder sound be heared from either of these stations?

now interference requires constant phase difference and since in both cases frequencies change at same rate shouldn't interference occur?

Actually, the interference between two waves, as they pass through each other, happens regardless of their frequencies: the signal at any point in space and time will be equal to the sum of the signals from the two waves.

Which means if 2 radio stations have same song being played shouldn't louder sound be heard from either of these stations?

If a filter of a radio receiver with a proper bandwidth, roughly $$80$$Hz in your example, is tuned to one of the two radio stations, it simply won't pass the signal from the other radio station, regardless of whether the first radio station is transmitting or not.

So, although radio waves will interfere on their way to the filter and even inside the filter, only one of the signals will pass through the filter and it won't be affected by the interference that happened earlier. This is because a filter is a linear element and its handling of a signal is not affected by the presence other signals.

To answer the question as posed in the title:

Commercial radio stations in any given geographic broadcast market are assigned frequencies that fully accomodate the bandwidth requirements of their signals, so they will not interfere with one another.

Those bandwidth requirements are a function of the carrier frequency and the information rate represented by the modulation of that carrier. These factors, along with the need to provide an adequate number of carrier frequency assignments within a given market area, then determine which portion of the radio frequency spectrum will be given over to that class of transmission.

In the example you cite- where the carrier frequency is actually below the audio frequency range or near the bottom of it- would never be used in practice and as such is an unrealistic case. Commercial FM spans the frequency band of 88 to 108 megahertz.

• but audible frequency range = 20 to 20,000 Hz ...F.M = 88,000,000 to 108,000,000 is'nt it still too high ? – Rix Vii Sep 22 '18 at 8:26
• it is high, but it was also available after the second world war, when FM was commercialized and the VHF frequency bands were allocated. – niels nielsen Sep 22 '18 at 18:44