A carrier wave is modulated by no. of sine waves with modulation indices ${m_1},{m_2},{m_3}.......$The total modulation index(m) of the wave is:
A) ${m_1} + {m_2} + {m_3} + .......$
B) ${m_1} - {m_2} + {m_3} + .......$
C) $\sqrt {m_1^2 + m_2^2 + m_3^2 + ......} $
D) \[\sqrt {\dfrac{{m_1^2 + m_2^2 + m_3^2 + ....}}{n}} \]

Hint: The ratio of a fundamental component amplitude of the line to the neutral inverter output voltage to the one half of the available voltage is called the Modulation Index.

Complete step by step solution:
Given modulation indices of the different modulating waves are ${m_1},{m_2},{m_3}.......$
Total modulation index, m =?
We know that a square-law device is a device that produces a current or an output voltage that is proportional to the square of the current or input voltage. They are mainly used in detectors and modulators. In simple terms it is a nonlinear device that produces a nonlinear output of the message and the carrier signal.
In simple terms, the Square law implies the input and output relation of the devices that are used for modulation.
Thus the total modulation index by the different number of sine waves from the square-law device is given as $m = \sqrt {m_1^2 + m_2^2 + m_3^2 + ......} $.

Hence the correct option is C.

Note: 1. The value of the modulation index must be 1 for the perfect modulation. Overmodulation is defined as the condition which is mostly found in telecommunication when the level of the modulating signal exceeds the value. It is dangerous and somewhat bad also.
2. The earliest modulation method that has been used in transmitting the information over the radio is Amplitude Modulation. In A M, the signal strength varies in proportion to the message signal like an audio signal.
3. Frequency modulation is better than Amplitude modulation. It will have higher bandwidth and hence the sound quality is much better in this.