Audio sine waves of 3 kHz frequency are used to amplitude modulate a carrier signal of 1.5 MHz. Which of the following statements are true?
Audio sine waves of 3 kHz frequency are used to amplitude modulate a carrier signal of 1.5 MHz. Which of the following statements are true?

(a) The sideband frequencies are 1506 kHz and 1494 kHz

(b) The bandwidth required for amplitude modulation is 6kHz

(c) The bandwidth required for amplitude modulation is 3 MHz

(d) The sideband frequencies are 1503 kHz and 1497 kHz.

Answer:

The correct options are :

(b) The bandwidth required for amplitude modulation is 6kHz

(d) The sideband frequencies are 1503 kHz and 1497 kHz.

Explanation:

We know that the AM wave contains three frequencies  and 
where  represents the carrier frequency and,
 and  represent the sideband frequencies.
 denotes the upper sideband (USB) frequency
denotes the lower sideband (LSB) frequency
According to the given question, the frequency of audio sine wave is given:
and the frequency of carrier signal is:
Now, by using above definitions the sideband frequencies can be determined in the following manner:
Upper sideband frequency is 1503kHz
Lower sideband frequency is 1497kHz
Also, the expression for the bandwidth is