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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?

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  • $\begingroup$ I think is and engineering question. eg electronics.stackexchange.com/questions/39481/… $\endgroup$
    – sammy gerbil
    Commented Sep 22, 2018 at 11:32
  • $\begingroup$ "now interference requires constant phase difference and since in both cases frequencies change at same rate should'nt interference occur ?" - your reasoning here is opaque to me. $\endgroup$
    – Alfred Centauri
    Commented Sep 22, 2018 at 12:23
  • $\begingroup$ Have you perused Frequency-division multiplexing? $\endgroup$
    – Alfred Centauri
    Commented Sep 22, 2018 at 12:25
  • $\begingroup$ Back in the late 1950s I was allowed to use a very sensitive radio receiver that could pick up stations broadcasting from many thousands of miles away. Often it picked up two distant stations using the same carrier frequency, and, indeed, there was interference easily discernable as the beat frequency - the difference frequency - between the two carriers. $\endgroup$
    – S. McGrew
    Commented Jan 18, 2021 at 3:19

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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.

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  • $\begingroup$ but audible frequency range = 20 to 20,000 Hz ...F.M = 88,000,000 to 108,000,000 is'nt it still too high ? $\endgroup$
    – Rix Vii
    Commented Sep 22, 2018 at 8:26
  • $\begingroup$ it is high, but it was also available after the second world war, when FM was commercialized and the VHF frequency bands were allocated. $\endgroup$
    – niels nielsen
    Commented Sep 22, 2018 at 18:44
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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?

Although the frequencies in your example are not realistic, your question still can be answered.

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.

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I had the same question when I first learned about the topic, I'm in no way an expert, but I totally get where your confusion comes from.

You misunderstood how information is encoded via modulation on a carrier wave

I will explain it but I would also suggest that you look again at this topic. The signal waves (waves that are/contain the information broadcasted) are no longer seperate waves but are encoded on the carrier, it is not simply the combination of multiple waves. Look at the difference between a combined wave and an modulated wave. In interference the wave at each point in time is the sum of the amplitudes. However in a radio signal the signal waves frequency no longer exists but was used to alter the carriers frequancy for FM and amplitude for AM. In both cases the frequency of the resulting wave is around the frequency of the carrier wave and the frequency of the signal wave no longer really exists. Therefore the signal can only be disturbed by waves of the same frequency for which the bandthwidhts exist. Even though signals can have equal frequencies, they are encoded at a different frequency.

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