Modern Physics 7 Question 23
24. The modulation frequency of an AM radio station is $250 kHz$, which is $10 %$ of the carrier wave. If another AM station approaches you for license, what broadcast frequency will you allot?
(Main 2019, 10 Jan II)
(a) $2000 kHz$
(b) $2250 kHz$
(c) $2900 kHz$
(d) $2750 kHz$
Show Answer
Solution:
- For a given carrier wave of frequency $f _c$ with modulation frequency $f _m$, the bandwidth is calculated by
$$ \begin{aligned} & f _{\text {upper }}=f _c+f _m \\ & f _{\text {lower }}=f _c-f _m \end{aligned} $$
To avoid overlapping of bandwidths, next broadcast frequencies can be
$$ f _1=f _c \pm 2 f _m, f _2=f _c \pm 3 f _m $$
So, next immediate available broadcast frequency is
$$ f _1=f _c+2 f _m \text { and } f _1^{\prime}=f _c-2 f _m $$
Given, $f _m=250 kHz$
and also that $f _m$ is $10 %$ of $f _c$, i.e. $f _c=2500 kHz$.
So, $f _1=2500+(2 \times 250)=3000 kHz$
and $f^{\prime}{ } _1=2500-(2 \times 250)=2000 kHz$
