JEE Main2016PhysicsCommunication SystemActual
A modulated signal C m t has the form C m t = 30 sin ⁡ 300 π t + 10 cos ⁡ 200 π t - cos ⁡ 400 π t . The carrier frequency f c , the modulating frequency (message frequency) f m , and the modulation index μ are respectively given by :
Options
- Af c = 200 H z ; f m = 50 H z ; μ = 1 2
- Bf c = 150 H z ; f m = 50 H z ; μ = 2 3
- Cf c = 150 H z ; f m = 30 H z ; μ = 1 3
- Df c = 200 H z ; f m = 30 H z ; μ = 1 2
Correct answer
B. f c = 150 H z ; f m = 50 H z ; μ = 2 3
Step-by-step solution
Compare with C m ( t ) = A c sin ( w c t ) + μ A c 2 [ cos ( w c − w m ) t − cos ( w c + w m ) ] μ A c 2 = 10 A c = 30 μ = 2 3 w c = 2 π f c = 300 π ⇒ f c = 150 H z w c − w m = 200 π w m = 100 π f m = 50 H z