Numerical - Calculation of frequency spectrum

An oscillator for an AM transmitter has a 100μH coil and a 10nF capacitor. If a modulating frequency of 10 KHz modulates the oscillator, find the frequency range of the side bands.
a.) 149 KHz to 169 KHz
b.) 184 KHz to 296 KHz
c.) 238 KHz to 296 KHz
d.) 155 KHz to 166 KHz

Correct Answer: a.) 149 KHz to 169 KHz

Explanation:

Carrier frequency f_c = 1/2Π√LC
= 1/ 2Π√100*10-6*10*10^-9
= 1/2Π*10^-6
= 1.59* 10⁵ Hz
= 159 KHz
The modulating frequency f_m is 10KHz
Therefore the range of AM spectrum is given by (f_c – f_m ) to (f_c + f_m )
= (159-10) to (159+10)
= 149 KHz to 169 KHz