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 :
[ Given , $c$ = speed of electromagnetic wave in vacuum/air ]

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

Answer 1

The correct option is D $\frac{c}{f_c}$

The equation of an amplitude modulated wave is given by :

$y=(A_c+A_m\sin {\omega }_{m}t)\sin {\omega }_{c}t$

Here , ${\omega }_c$ $=$ angular frequency of modulated signal

Thus , frequency of modulated signal $=$ $f_c$

Hence , wavelength ($\lambda$) $=$ $\frac{v}{f}$ $=$ $\frac{c}{f_c}$

Option (d) is the correct answer .