1)

A message signal is used to modulate a carrier signal of frequency  5 MHz and peak voltage of 40 V . In the process, two side-bands are produced separated by 40 kHz. If the modulation  index is 0.75, then the peak voltage  and frequency of the messages  signal, respectively are

A) 60 V, 10 kHz

B) 60 V, 20 kHz

C) 30 V, 10 kHz

D) 30V, 20 kHz

Option D

### Explanation:

Given, frequency of carrier signal , f=5 MHz  and peak voltage , $V_{c}$= 40V

Modulation index , $\mu$ =0.75

$\therefore$           $\mu=\frac{V_{m}}{V_{c}}$          [$\because V_{m}$   is peak voltage of message signal]

$0.75 =\frac{V_{m}}{40}$

$\Rightarrow$           $V_{m}=40 \times 0.75$

$V_{m}=30V$

Since, a difference of frequencies of two sidebands is equal to the bandwidth  (2 fm).

i.e, Band width =40 kHz

$2f_{m}=40kHz \Rightarrow f_{m}=20kHz$

Hence, the peak voltage and frequency will be 30V and 20 kHz