Question

If $f_{m}$ is a modulating frequency and $f_{c}$ is carrier wave frequency, then Bandwidth in Amplitude Modulated wave is

• A. $2f_{c}$
• B. $f_{c} + f_{m}$
• C. $2f_{m}$
• D. $\frac{(f_{c} + f_{m})}{2}$

Hint:

Bandwidth of an AM signal is always independent of the carrier frequency value and equals exactly twice the message frequency: $\text{BW} = 2 \times f_{\text{message}}$.

Answer 1

The Correct Option is C

Step 1: What AM creates.
In amplitude modulation a carrier $f_{c}$ is mixed with a signal $f_{m}$. This makes extra side frequencies.

Step 2: The two sidebands.
They are the upper sideband $f_{c} + f_{m}$ and the lower sideband $f_{c} - f_{m}$.

Step 3: Meaning of bandwidth.
Bandwidth is the gap between the highest and lowest frequencies in the wave.

Step 4: Find the highest and lowest.
Highest is $f_{c}+f_{m}$ and lowest is $f_{c}-f_{m}$.

Step 5: Subtract them.
\[ \text{BW} = (f_{c}+f_{m}) - (f_{c}-f_{m}) = 2f_{m} \]
Step 6: State the answer.
So the bandwidth is $2f_{m}$, which is option 3.
\[ \boxed{\text{BW} = 2f_{m}} \]