Products
Rewards 
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Please sign up to our reward program to support us in return and take advantage of the incredible listed offers.

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY 
BUSINESS MANAGER

Advertise your business, and reach millions of students around the world.

HOLOOLY 
TABLES

All the data tables that you may search for.

HOLOOLY 
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY 
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY 
HELP DESK

Need Help? We got you covered.

Chapter 1

Q. 1.1.6

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal S(t) = 5 cos 1600πt + 20cos1800πt + 5cos2000πt. The value of the modulation index is _____.

Step-by-Step

Verified Solution

AM

\begin{aligned}S(t) &=A_{c} \cos 2 p f_{c} t\left[1+k_{a} m(t)\right] \\S(t) &=A_{c} \cos 2 p f_{ c } t\left[1+k_{a} A_{m} \cos 2 \pi f_{m} t\right] \\S(t) &=A_{c} \cos 2 p f_{c} t+\frac{A_{c} \mu}{2} \cos 2 \pi\left(f_{c}+f_{m}\right) t \\&+\frac{A_{c} \mu}{2} \cos 2 \pi\left(f_{c}-f_{m}\right) t\end{aligned}

Comparing the above standard equation with given equation, we get

\begin{aligned}f_{c} &=900 Hz \\f_{m} &=100 Hz \\A_{c} &=20 \\\frac{A_{c} \mu}{2} &=5 \\A_{c} \mu &=10\end{aligned}

 

\begin{aligned}&\mu=\frac{10}{A_{c}}=\frac{10}{20} \\&\mu=\frac{1}{2}=0.5.\end{aligned}

Hence, the correct Answer is (0.5).