Question

If the highest frequency modulating a carrier is $5\mathrm{kHz}$, then the number of AM broadcast stations accommodated in a $90\mathrm{kHz}$ bandwidth is ___________.

Answer 1

Step 1 Given data:

The highest frequency modulating a carrier is $5\mathrm{kHz}$.

The highest bandwidth is $90\mathrm{kHz}$.

Step 2 Formula used:

$\mathrm{Number}\mathrm{of}\mathrm{stations}=\frac{\mathrm{Total}\mathrm{B}.\mathrm{W}}{2\times \mathrm{Band}\mathrm{width}\mathrm{for}\mathrm{each}\mathrm{channel}}$

Step 3 Number of stations

The total bandwidth is $90\mathrm{kHz}$.

Bandwidth for each channel is $5\mathrm{kHz}$.

That is,

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{stations}=\frac{\mathrm{Total}\mathrm{B}.\mathrm{W}}{2\times \mathrm{Band}\mathrm{width}\mathrm{for}\mathrm{each}\mathrm{channel}} \\ \mathrm{Number}\mathrm{of}\mathrm{stations}=\frac{90}{2\times 5} \\ \mathrm{Number}\mathrm{of}\mathrm{stations}=\frac{90}{10} \\ \mathrm{Number}\mathrm{of}\mathrm{stations}=9 \end{gathered}$$

Hence, if the highest frequency modulating a carrier is $5\mathrm{kHz}$, then the number of AM broadcast stations accommodated in a $90\mathrm{kHz}$ bandwidth is 9.