Question

If a message signal of frequency '$f_m$' is amplitude modulated with a carrier signal of frequency '$f_c$' and radiated through an antenna, the wavelength of the corresponding signal in air is:

• A. $\frac{c}{f_c - f_m}$
• B. $\frac{c}{f_c + f_m}$
• C. $\frac{c}{f_c}$
• D. $\frac{c}{f_m}$

Hint:

In any modulation scheme (AM, FM, etc.), the purpose of the high-frequency carrier wave is to be the primary signal that is radiated. The message is encoded onto this carrier. Therefore, the physical properties of the radiated wave, like its wavelength, are determined by the carrier frequency.

Answer 1

The Correct Option is C

In amplitude modulation (AM), a low-frequency message signal ($f_m$) modulates a high-frequency carrier signal ($f_c$).
The resulting AM signal contains three frequency components: the carrier frequency ($f_c$), the upper sideband ($f_c + f_m$), and the lower sideband ($f_c - f_m$).
Typically, the carrier frequency is much higher than the message frequency ($f_c \gg f_m$).
The signal that is radiated by the antenna is an electromagnetic wave. The vast majority of the power in an AM signal is concentrated at the carrier frequency.
The wavelength ($\lambda$) of an electromagnetic wave is related to its frequency ($f$) and the speed of light ($c$) by the formula $\lambda = \frac{c}{f}$.
Since the dominant frequency being transmitted is the carrier frequency, the wavelength of the radiated signal is determined by $f_c$.
Therefore, the wavelength is $\lambda = \frac{c}{f_c}$.