Modern Physics Ques 270
- 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 $ $kHz$
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Answer:
Correct Answer: 270.(a)
Solution:
Formula:
- 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 $ $kHz$
BETA
