Question

An oscillator is producing FM waves of the frequency \[2kHz\] with a variation of \[10kHz\] . The modulating index is equal to
(A) \[0.20\]
(B) \[5.0\]
(C) \[0.67\]
(D) \[1.5\]

Answer 1

Hint The FM modulation index is adequate to the ratio of the frequency deviation to the modulating frequency. In the question, the value of frequency deviation and modulating frequency is already provided. Hence we can just put the values and calculate the answer.
Formula used: ${m_f} = \dfrac{{Frequency\,deviation}}{{Modulating\,frequency}}$

Complete Step by step solution
Modulating index, ${m_f} = \dfrac{{Frequency\,deviation}}{{Modulating\,frequency}}$
Given,
Frequency deviation \[ = 10kHz\],
Modulating frequency $ = 2kHz$
By substituting the values we get,
${m_f} = \dfrac{{10kHz}}{{2kHz}} = 5$

Hence option B. is the correct answer.

Additional Information
Let us consider a simple single-frequency sinusoidal wave which is called the carrier wave. This wave contains different parameters like amplitude, frequency, and the phase difference. When any one of these three parameters is varied or modulated, we get frequency- modulated waves(FM), amplitude modulated waves(AM), and phase- modulated waves(PM) respectively.
The process of encoding information in a carrier wave by changing the instantaneous frequency of the wave is known as Frequency Modulation (FM). The term and technology are utilized in computing, signal processing , and telecommunications.
The main use of modulating frequency is in FM radio broadcasting. An advantage of FM in radio transmission is that it has a greater signal-to-noise ratio and thus rejects frequency interference better than an equal power Amplitude Modulation (AM) signal. Therefore music is mostly broadcasted over FM radio.
Frequency modulation and PM (phase modulation) are the complementary principal methods of angle modulation; PM is usually used as an intermediate step to realize FM. These methods contrast with AM, during which the amplitude of the carrier wave varies, while the frequency and phase remain constant.

Note
The physical significance of the modulation index is that it is used to determine the strength and quality of the transmitted signal. If the modulation index is little, then the quantity of variation within the carrier amplitude is little.