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) $2750 kHz$

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Solution:

  1. 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 $f^{\prime}{ } _1=2500-(2 \times 250)=2000 kHz$



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