Question

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?
1. 2000 kHz
2. 2250 kHz
3. 2900 kHz
4. 2750 kHz

Answer 1

Correct Answer - Option 1 : 2000 kHz

Concept:

For a given carrier wave of frequency f_c with modulation frequency f_m, the bandwidth is calculated by

f_upper = f_c + f_m

f_lower = f_c – f_m       ----(1)

To avoid overlapping of bandwidths, next broadcast frequencies can be

f₁ = f_c ± 2f_m

f₂ = f_c ± 3f_m and so on

So, next immediate available broadcast frequency is f₁ = f_c + 2f_m and \(f_1' = {f_c} - 2{f_m}\)

So,

f₁ = f_c + 2f_m

Calculation:

Given,

Modulation frequency, f_m = 250 kHz

f_m is 10% of f_c

i.e., f_m = 10% of f_c

\(250\;kHz = \frac{{10}}{{100}} \times {f_c}\) 

2500 = f_c

f_c = 2500 kHz

And also that f_m is 10% of f_e, i.e f_e = 2500 kHz

So, f₁ = 2500 + (2 × 250)

f₁ = 2500 + 500 = 3000 kHz

Now,

\(f_1' = {f_c} - 2{f_m}\) 

\(f_1' = 2500 - \left( {2 \times 250} \right)\) 

\(f_1' = 2500 - 500 = 2000\) kHz

Therefore, if another AM station approaches us for license, the lowest broadcast frequency which we can allot is 2000 kHz.