Q.A bandwidth of 15 MHz is available for AM transmission. If the maximum audio signal frequency used for modulating the carrier is not to exceed 15 kHz. How many stations can be accommodated within this band simultaneously without interfering with each other?

A frequency spectrum is a graph of amplitude against frequency. Because an AM wave is the sum of a carrier and two side frequencies, its spectrum is just three vertical lines: the carrier at $f_c$ with height $V_C$, a lower side frequency at $f_c - f_m$ and an upper side frequency at $f_c + f_m$, each of height $m_a V_C/2$, spaced equally on either side of the carrier.

The two side frequencies are the sidebands — the sum-and-difference signals produced by modulation. A key idea for the II PUC Electronics exam is that the carrier itself carries no information; the entire message resides in the sidebands. That is why the transmission of sidebands is essential — suppressing both sidebands would leave nothing but an information-free carrier.

The bandwidth of the AM wave is the frequency range from the lowest to the highest side frequency:

$BW = (f_c + f_m) - (f_c - f_m) = 2 f_m$ …