If the amplitude of modulating signal is kept constant then the modulation index is proportional to the:

  1. amplitude of carrier wave
  2. (amplitude of ​carrier wave)-1
  3. (amplitude of ​carrier wave)2
  4. None of these

Answer (Detailed Solution Below)

Option 2 : (amplitude of ​carrier wave)-1
Free
CRPF Head Constable & ASI Steno (Final Revision): Mini Mock Test
40 Qs. 40 Marks 45 Mins

Detailed Solution

Download Solution PDF

CONCEPT:

Amplitude modulation:

  • In amplitude modulation, the amplitude of the carrier wave is varied in accordance with the information signal.
  • Here we explain the amplitude modulation process using a sinusoidal signal as the modulating signal.
  • Let c(t) = Acsin(ωct) represent carrier wave and m(t) = Amsin(ωmt) represent the message or the modulating signal.
  • So the modulated signal can be represented as,

⇒ cm(t) = [Ac + Am.sin(ωmt)].sin(ωct)

⇒ cm(t) = [Ac + μAc.sin(ωmt)].sin(ωct)

Where Ac = amplitude of the carrier wave, Am = amplitude of the modulating signal, ωc = angular frequency of the carrier wave, ωm = angular frequency of the modulating signal, and μ = modulation index

  • The modulation index is given as,

  • In practice, μ is kept  to avoid distortion.
  • Using the trignomatric relation 2sinA.sinB = cos(A - B) - cos(A + B), we can represent the modulated signal as,

  • Here (ωc - ωm) and (ωc + ωm) are respectively called the lower side and upper side frequencies.
  • The modulated signal now consists of the carrier wave of frequency ωc plus two sinusoidal waves each with a frequency slightly different from ωc, known as sidebands.

  • As long as the broadcast frequencies (carrier waves) are sufficiently spaced out so that sidebands do not overlap, different stations can operate without interfering with each other.

EXPLANATION:

  • We know that if c(t) = Acsin(ωct) represent carrier wave and m(t) = Amsin(ωmt) represent message signal, then the modulation index is equal to the,

Where Ac = amplitude of the carrier wave, and Am = amplitude of the modulating signal

  • If the amplitude of modulating signal is kept constant then,

  • Hence, option 2 is correct.

Latest Indian Coast Guard Navik GD Updates

Last updated on Jul 4, 2025

-> The Indian Coast Guard Navik GD Application Correction Window is open now. Candidates can make the changes in the Application Forms through the link provided on the official website of the Indian Navy.

-> A total of 260 vacancies have been released through the Coast Guard Enrolled Personnel Test (CGEPT) for the 01/2026 and 02/2026 batch.

-> Candidates can apply online from 11th to 25th June 2025.

-> Candidates who have completed their 10+2 with Maths and Physics are eligible for this post. 

-> Candidates must go through the Indian Coast Guard Navik GD previous year papers.

Hot Links: teen patti real money app teen patti yas teen patti gold apk download teen patti master 2023 teen patti online game