Picture of the day: 802.11 channels in 2.4GHz band. (Source)
We use a frequency range because in our modulation of and demodulation of a single bit for example we use different frequencies. So, in fact we need to specify a range for our channel. On the other hand to make sure we can distinguish between frequency components of different neighboring channels we need to distant them to make sure we can unambiguously decide which channel a frequency being used belongs to.
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The problem was that I thought that with a single frequency like in a sinosoid we can send our data and we do not need a frequency range.
Please don't forget that "bandwidth" is the frequency range of the channel. Here we have shannon's formula for channel capacity:
C = B log(1 + S/N) C = Channel bi trate, B = Bandwidth (frequency range) S/N = Signal to noise ratio
This means that if you have a range of 15KHz bandwidth available at the center frequency of 100KHz and on the other hand you have 15KHz of bandwidth available at the center frequency of 1MHz : based on Shannon's formula in ideal case disregarding modulation and demodulation scheme both will give you the same bit rate since capacity does not depend on where you're frequency is but rather how big of a range of frequency you have available.
