An amplitude moduated signal consists of a message singnal of frequency 1 KHz and peak voltage of 5 V , moduating a carrier frequency of 1 MHz and peak voltage of 15 V . The correct description of this singnal is

Options

A. `5[ 1+3 sin ( 2 pi 10 ^6 t ) ] sin ( 2 pi 10 ^(3) t)`
B. `15 [ 1 + 1/3 sin ( 2 pi 10 ^3 t) ] sin ( 2 pi 10 ^6 t)`
C. `[5 + 15 sin ( 2 sin ( 2 pi 10 ^3 t) ] sin ( 2 pi 10 ^6 t)`
D. `[ 15 + 5 sin ( 2 pi 10 ^6 t) ] sin (2 pi 10 ^3 t)`

Answer

B

Explanation

Given ,
Frequency of message signal `( F_(m )) = 1 KHz`
`= 1xx10 ^3 Hz`
Peak voltage of message singnal `(E_m) = 5 V `
Carrier frequency ` ( f_c) = 1MHz = 1xx 10 ^6 Hz`
Peak voltage of carrier `(E_c) = 15 V`
We know that , the equation of amplitude modulated wave is given by
` e(t) = E_C [ 1 +(E_m) /(E_C) sin omega _(m^t) ] sin omega _c t`
` =E_(C ) [ 1 + (E_m )/(E_C ) sin ( 2 pi f _(m) x ] sin 2 pi f_c t `
` = 15 [1+ 1/3 sin (2 pi 10 ^3 t) ] sin 2 ( pi 10 ^6 t)`