Question

A 1000 kHz carrier is simultaneously modulated with 300 Hz and 250 Hz audio waves. Which of the following frequencies will not be present in the output?

• A. \(700\,kHz\)
• B. \(998\,kHz\)
• C. \(999.7\,kHz\)
• D. \(1000.3\,kHz\)

Hint:

AM produces frequencies only near carrier (fc ± fm).

Answer 1

The Correct Option is A

Concept: In amplitude modulation: \[ f_{sidebands} = f_c \pm f_m \]

Step 1: Given data Carrier frequency: \[ f_c = 1000\,kHz \] Modulating frequencies: \[ f_{m1} = 300\,Hz,\quad f_{m2} = 250\,Hz \]

Step 2: Convert units \[ 300\,Hz = 0.3\,kHz,\quad 250\,Hz = 0.25\,kHz \]

Step 3: Calculate sidebands \[ 1000 \pm 0.3 \Rightarrow 999.7\,kHz,\ 1000.3\,kHz \] \[ 1000 \pm 0.25 \Rightarrow 999.75\,kHz,\ 1000.25\,kHz \]

Step 4: Compare with options All valid frequencies are close to carrier frequency.

Step 5: Identify incorrect \[ 700\,kHz \text{ is far from carrier ⇒ not possible} \]

Final Answer: \[ \boxed{700\,kHz} \]