Question

If the modulation index is $\dfrac{1}{2}$ and the power of the carrier wave is 2W. What is the total power of a modulated wave?
A) 0.5W
B) 1W
C) 0.25W
D) 2.25W

Answer 1

The power of the carrier wave is given and the modulation index of the wave is given. We know, the total formula depends on both these terms and no other quantities. Therefore, substituting these in the total power formula will give the result.
Formula used:
${{P}_{T}}={{P}_{c}}(1+\dfrac{{{m}_{a}}^{2}}{2})$

Complete answer:
We know the value of modulation index and the power of the carrier wave,
They are,
${{P}_{c}}=2W,{{m}_{a}}=\dfrac{1}{2}...(1)$
Now, we know the formula of total power is equal to,
${{P}_{T}}={{P}_{c}}(1+\dfrac{{{m}_{a}}^{2}}{2})...(2)$
Substituting the values of equation (1) in equation (2),
$\begin{aligned} & {{P}_{T}}={{P}_{c}}(1+\dfrac{{{m}_{a}}^{2}}{2}) \\\ & {{P}_{T}}=2(1+\dfrac{{{(0.5)}^{2}}}{2}) \\\ & {{P}_{T}}=2\times \dfrac{9}{8} \\\ & {{P}_{T}}=2.25W \\\ \end{aligned}$

So, the correct answer is “Option D”.

Additional Information:
Carrier wave in telecommunications is a waveform that is modulated with an information bearing signal for the purpose of conveying information. The carrier wave is usually having higher frequency than the input waves frequency. The carrier waves purpose is to transmit the information through space in the form of an electromagnetic wave. It also allows other several carriers of different frequencies to share a common physical transmission medium by frequency division multiplexing. The term carrier wave first originated in radio communication, where the carrier wave creates radio waves that carry information through air from transmitter to receiver.

Note:
The carrier wave given in the above question has some amount of modulation. The carrier waves SPSthat don’t have any modulation don’t transport or carry information from one place to other places. Modulation index plays an Important role in transporting the information.