Question

The modulation frequency of an AM radio station is 250KHz, which is 10% of the carrier wave. If another AM station approaches you for licence what broadcast frequency will you allot?
(A) 2750 KHz
(B) 2250 KHz
(C) 2900 KHz
(D) 2000 KHz

Answer 1

The modulating frequency is given, first of all we will calculate the carrier frequency from modulating frequency.Then , we will calculate the range of both the frequencies , and of the frequencies are not overlapping , that will be allotted to the other customer.

Complete step by step answer:
Modulation frequency $= 250$ KHz , this is 10% of carrier wave frequency. The carrier wave frequency will be ${f_c}$ .
${f_c} = \dfrac{{250}}{{0.1}} = 2500$
$\Rightarrow{f_c} = 2500$ KHz.
The range of frequencies will be from ${f_c} - {f_m}$ to ${f_c} + {f_m}$ .
Range= $2500 - 250$ to $2500 + 250$
Range= $2250$ to $2750$KHz.
The above is the range of one radio station. Now if the second radio station approaches you, you will give the frequency range that is not overlapping with the previous one. Now, this eliminates two option i.e. B and D. We will now consider two options.
Let us consider ${f_c} = 2900$ KHz . Then
${f_m} = \dfrac{{10}}{{100}} \times 2900 \\\ \Rightarrow{f_m} = 290 \\\$
The range ${f_c} - {f_m} = 2900 - 290 \\\ {f_c} - {f_m} = 2610 \\\$
This will overlap the given signal.
Now consider the other option where ${f_c} = 2000$ KHz
${f_m} = 200$ KHz
The range of the signal,
${f_c} - {f_m} = 1800 \\\ \therefore{f_c} + {f_m} = 2200 \\\$
We can clearly see that this frequency doesn’t overlap with the given signal.

The correct option is D.

Note: Keep in mind all the frequencies given in the options are carrier frequencies and not modulated ones. They shall be calculated as per the given relation i.e. one-tenth of carrier frequency.The sum of the carrier frequency and the modulating frequency ( ${f_c} + {f_m}$ ) is called upper side frequency. The difference of the carrier frequency and the modulating frequency ( .${f_c} - {f_m}$. ) is called lower band frequency.