Question

If a message signal of frequency$\text{'}{f}_m\text{'}$ is amplitude modulated with a carrier signal of frequency $\text{'}{f}_c\text{'}$ and radiated through an antenna, the wavelength of the corresponding signal in the air is:

Given, $C$ is the speed of electromagnetic waves in vacuum/air

• A. $\frac{C}{\left(f_c+f_m\right)}$
• B. $\frac{C}{\left(f_c-f_m\right)}$
• C. $\frac{C}{f_m}$
• D. $\frac{C}{f_c}$

Answer 1

The correct option is D

$\frac{C}{f_c}$

Step 1: Given data:

If a message signal of frequency$\text{'}{f}_m\text{'}$ is amplitude modulated with a carrier signal of frequency $\text{'}{f}_c\text{'}$ and radiated through an antenna.

Step 2: Formula used:

Recognize the amplitude-modulated wave equation$y=\left(A_c+A_m\sin {\omega }_{m}t\right)\sin {\omega }_{c}t$.

Here, the signal's angular frequency is modulated$={\omega }_c$.

Consequently, the modified signal's frequency $=f_c$

Therefore the wavelength is$=\frac{C}{f_c}$.

Hence, the correct option is (D).