Given below are two statements :

Statement I : A speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.

Statement II : The side band frequencies are 1002 kHz and 998 kHz.

In the light of the above statements, choose the correct answer from the options given below :

CONCEPT:

• Bandwidth is defined as the difference between the upper and lower frequencies in continuous bands of frequencies and the formulation of bandwidth frequency is written as;

          Bandwidth = 2 f_m

          here we have fm is the modulation frequency or a signal frequency.

• The side frequencies are written as;

           (fc + fm) and (fc - fm)

            Here we have fm is the modulation frequency or a signal frequency, fc is the carrier frequency.

EXPLANATION:

The statement " I "  said that a speech signal of 2 kHz is used to modulate a carrier signal of 1 MHz. The bandwidth requirement for the signal is 4 kHz.

As we know, Bandwidth = 2fm    -----(1)

Given: Modulation frequency,fm = 2 kHz

Now, on putting the value in equation (1) we have;

Bandwidth = 2×2  

⇒ Bandwidth = 4 kHz

Therefore, the statement " I " is correct.

The statement "II" said that the sideband frequencies are 1002 kHz and 998 kHz.

The side frequencies are written as;

Given: (fc + fm) = 1002 kHz

and (fc - fm) = 998 kHz.

Now,  (fc + fm) = 1002 kHz 

⇒(fc + fm) = 1000 + 2 = 1002 kHz 

and (fc - fm) = 1000 - 2 = 998 kHz

Therefore, statement "II" is correct.

Hence, option 1) is the correct answer.