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 :

Options

A. `(c )/(f_(c )-f_(m))`
B. `(c )/(f_(m))`
C. `(c )/(f_(c )+f_(m))`
D. `(c )/(f_(c ))`

Answer

To find the wavelength of the amplitude-modulated signal radiated through an antenna, we can follow these steps:

### Step 1: Understand the concept of Amplitude Modulation (AM)
In amplitude modulation, a message signal of frequency \( f_m \) is used to modulate a carrier wave of frequency \( f_c \). The resulting signal contains both the carrier frequency and the sidebands created by the modulation.

### Step 2: Identify the relevant formula for wavelength
The wavelength \( \lambda \) of a wave is related to its frequency \( f \) and the speed of light \( c \) in air (or vacuum) by the formula:
\[ \lambda = \frac{c}{f} \]
where:
- \( \lambda \) is the wavelength,
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( f \) is the frequency of the wave.

### Step 3: Determine the frequency of the modulated signal
In amplitude modulation, the frequency of the modulated signal is the frequency of the carrier wave \( f_c \). The message signal frequency \( f_m \) does not affect the wavelength of the carrier wave.

### Step 4: Calculate the wavelength
Using the formula from Step 2, we can substitute \( f \) with \( f_c \):
\[ \lambda = \frac{c}{f_c} \]
This gives us the wavelength of the amplitude-modulated signal.

### Conclusion
Thus, the wavelength of the corresponding signal in air is:
\[ \lambda = \frac{c}{f_c} \]